Shapari User’s Guide


Introducing Shapari
What it is
What it is not
Who its for
System Requirements
Quick Start
Program Operation
Built-in Instructions
Name and Level
Displaying Shapes
Selecting Colors
Mixing Colors
Creating Patterns from Shapes
The Shape Matching Game
Reviewing Shape History
Saving Work in the Gallery
Overlaying Shapes
Customizing Shape Manipulators
Color Mapping

Introducing Shapari

What it is


  • A program that displays shapes and manipulates them in ways that only a computer can.
  • A program capable of producing intriguing, often stunning patterns, from very simple shapes and operations.
  • A conceptually simple but none-the-less challenging shape matching game.
  • A light exploration of many mathematical concepts including shape, size, count, multiplication, symmetry, transformations, periodicity, convergence, exponential growth, recursion and fractal geometry.
What it is not


Shapari is not a traditional drawing or paint program. It does not offer a broad compliment of tools that allow the creation of arbitrary drawings. There are already plenty of programs that do that quite well. Instead it offers a very limited set of simple tools which can be used to produce a surprisingly diverse range of patterns. Creating patterns with Shapari is more akin to brainstorming than deliberate, detailed design.

Shapari is not designed to help master any specific learning objectives. Rather, it is intended to foster abstract thinking and the exploration of mathematical concepts. It can certainly be educational, even enlightening at times.

Who its for


Shapari is designed for curious minds of all ages. Simple, directly accessible (no menu trees) controls allow the youngest users, just gaining competence with the mouse, to feel a sense of accomplishment displaying, coloring and manipulating shapes. Intermediate users can play the shape matching game, create interesting patterns, save and print them. Advanced users can create their own shape manipulators using a graphical editor and/or mathematical descriptions. These manipulators can then be applied iteratively to create fractal patterns.



  • Both structured (matching game) and unstructured (shape/pattern production) activities.
  • Both individual and partner play.
  • Multiple levels to support a range of user capabilities.
  • A graphical gallery that enables novice users to save their work without having to master file operations.
  • Automatic, transparent compression of saved work.
  • Individualized settings (name, level and gallery) for multiple users.
  • An intuitive, fun color selection mechanism
  • An innovative drawing history display
  • Multi-level undo
System Requirements


  • 80486 Microprocessor (Pentium recommended)
  • 640 x 480 Monitor Resolution (or better)
  • 256 Display Colors (or greater)
  • Microsoft Windows 95/98 or NT Operating System

Note: All Shapari displays are scaleable, in other words they appear essentially the same at all common screen resolutions. They are of course sharper at higher resolution. Color resolution is a different matter. Shapari drawings contain at most 256 colors, regardless of your system color settings. Higher color resolutions are useful primarily to programs wishing to achieve photo-realism.

Quick Start


People have very different learning styles when it comes to computer programs. If you (or your child) like to learn through experimentation, reading this section should be sufficient to get you on your way. For others, the Program Operation section that follows will also be of interest.

Most Shapari program actions are triggered by clicking on screen “buttons” (screen areas containing an icon and given a raised appearance). These buttons come in a variety of shapes and sizes. Buttons are sometimes grayed (drained of color) to indicate that they are not active in the current program state. For example, the undo button before anything has been done. Some actions are initiated by clicking on icons that do not have the raised button appearance. In either case, pointing to a button or icon with the mouse and lingering for a few seconds will display a descriptive label.

With just a few exceptions, clicking the left mouse button triggers Shapari actions. (For novice mouse users it may be helpful to put a small sticker on this button). The exceptions are all limited to levels 4 and 5 where right clicking in selected locations displays context menus which support the definition and management of custom shape manipulations. See the “Customizing Shape Manipulators” section for more details.

The question mark button that appears near the lower right corner of every program screen provides access to brief instructions relevant to whatever screen is being displayed.

Program Operation

This section provides a feature-by-feature description of the program. For each feature the mechanics are described first. Many of the descriptions then go on to suggest aspects that might be of interest at various ability levels.

Built-in Instructions


While this user’s guide is the most comprehensive source of program information, considerable resources are also built directly into the program. These include on-screen operating instructions and built-in demonstrations. The on-screen instructions, while relatively terse, have the advantage of pointing directly to relevant screen locations.

Clicking the question mark button near the lower right corner of any program screen or major dialog displays the relevant operating instructions. You can also display these instructions by pressing the F1 key at any time. The instructions are hyper-linked, with certain highlighted words serving as links other portions of the instructions. The instruction pages can also be navigated by clicking on the arrow icons appearing at the bottom of each page or by using the keyboard navigation keys including PageUp, Page Down, Home and End.

To dismiss the instructions, click the stop icon that appears among the navigation icons. The instructions will also be dismissed automatically if you click anywhere outside the instruction text and navigation areas. Shapari remembers your place, returning to it the next time you display the instructions. This makes it relatively easy to interleave instruction reading with program experimentation.

The built-in instructions are divided into five distinct sections, one for each of the following screens or dialogs:

  • Main
  • Name and Level Dialog
  • Pattern Review
  • Pattern Gallery
  • Manipulator Editor

There is no linkage between these sections.

The main instruction section provides access to the built-in demonstrations. There are demonstrations covering each of the following topics:

  • Pattern Creation
  • Matching Game
  • Editing Manipulators
  • Mixing Colors

To launch a demonstration click on one of the “Show” icons appearing on the instruction pages. Once a demonstration is launched, the program will take control of the mouse pointer, moving it around the screen and simulating clicks to carry out specific tasks. If you need to regain control of the mouse before a demonstration is finished, press the Ctrl and Esc keys simultaneously to interrupt the demonstration. A message reminding you of this key sequence appears on the title bar while the demonstration is in progress.

Name and Level


Shapari offers 5 levels of operation. The levels are distinguished primarily by the complexity of the shape manipulations available. Specific features of each level are summarized in a table at the end of this section. The table is best understood after reading the remainder of this guide.

To choose the desired level, invoke the level selection dialog by clicking on the button bearing the staircase icon (the second round button from the left near the bottom of the screen).

The dialog stores individual level selections for any number of users, including one anonymous user. The anonymous user level is selected by simply clicking one of the numbered level buttons appearing on the staircase. In response a brown dot, moves up/down the stairs until it rests on top of the step representing the selected level. The level can also be adjusted by dragging the brown dot up or down the staircase.

To add a named user, type the name in the edit box provided and press Enter. If the edit box is not visible, click on the words “New Name” to activate it. Once the new name has been added, it appears on the staircase as well as on the list. Select the appropriate level for the new user by clicking a level button or dragging the name to the desired step.

When the name list contains multiple entries, you can use the mouse or navigation keys to change the current user selection. The current selection is indicated by the appearance of an arrow to its left. The corresponding level can be changed at any time. Furthermore, the name itself can be edited by reselecting the current name with the mouse or by pressing Enter.

The significance of user names extends beyond storing individual levels. For each named user, Shapari provides private storage for drawings (see Saving Work in the Gallery) and custom shape manipulators (see Customizing Shape Manipulators).

To remove a name from the list, select it and press the delete (Del) key. If the user being removed has saved work in the gallery or customized the shape manipulators, you will be given the choice of leaving his/her data intact (on the hard disk) for possible reinstatement or deleting it.

Once your have made any desired changes to the user list and/or level, click the check-mark button at the bottom of the dialog to put the changes into effect. To discard all changes click the X-mark button instead.

Level Summaries

Level Features (cumulative)
1 Manipulators that produce one to five symmetrically scaled copies

Maximum of 2 steps for the matching game

2 Manipulators that reflect and scale asymmetrically (compress)

Maximum of 4 steps for the matching game

3 Manipulators that rotate and skew

Manipulators that include abutting copies

Maximum of 6 steps for the matching game

4 Manipulators that include overlapping copies

Multiple pages of manipulators

Ability to customize manipulators

5 Color mapping via color cycles (in place of matching game)
Displaying Shapes


Displaying shapes with Shapari is easy as can be. Just click any of the 15 shape buttons appearing at the upper left of the screen. The selected shape instantly appears in the circular drawing area in the center of the screen.


The youngest users can get a degree of satisfaction from the ability to make their favorite shapes appear at will. Slightly older users can learn to recognize and name some basic shapes. Others will be surprised to discover how much can be done with this limited set of shapes.

Selecting Colors


The color wheel appearing toward the lower left of the screen is used to select the color used to draw the next shape or color an existing shape. To pick a color, simply click on the portion of the color wheel showing the desired color. Upon releasing the mouse button, the wheel will spin until the desired color appears at the tip of the crayon shaped pointer. Until the button is released, the mouse may be dragged around to choose a different color. Once a selection is made, the color of the crayon pointer changes to reflect it. Black and white may be selected by clicking the hub and outer ring of the color wheel, respectively.


The color wheel organization encourages young users to think of colors in terms of their relationships to one another (lighter, darker, contrasting etc.)



When the mouse pointer moves to the circular drawing area it changes from an arrow to a crayon. The crayon color matches the current color wheel selection. Clicking on any drawing region changes its color to the selected color. The behavior is like that of the fill tool in a typical paint program. If the colored region extends to the outer edge of the drawing area, the selected color becomes the new background color. Note: When a shape is drawn using the same color as the background, it is outlined with a contrasting color so that it is visible.


Since the crayon appears automatically when the mouse is moved over the drawing area (no fill tool selection is required). This makes coloring accessible to the youngest users. They appreciate coloring because it enables them to make dramatic changes with a simple click. Intermediate and advanced users can create interesting patterns by interleaving coloring and shape manipulations. Refer to the discussion of shape manipulation for more information.



Coloring, as described above, can require a relatively high degree of dexterity, depending on the size of the region being colored. It is easy to make mistakes. The Eraser icon, which appears just above the coloring wheel, makes it easy to correct them. Just click on the eraser to undo the previous coloring or shape display. Click the eraser repeatedly to undo successive colorings or shape displays. Note that the undo button, which appears at the bottom right of the drawing area, applies to shape manipulations not coloring operations. Its behavior is described fully elsewhere.

Mixing Colors


The color wheel makes 38 color choices available with a single click. Additional colors can be obtained using the mixer that appears to the upper left of the color wheel. To mix two colors proceed as follows:

  1. Select the first color by clicking it on the color wheel.
  2. Move the mouse to the recessed area of the mixer. The cursor becomes a crayon.
  3. Click to deposit the selected color.
  4. Select the second color on the color wheel.
  5. Click the mixer recess again. An intermediate color appears in the recess.

To use the mixed, color click anywhere on the brown area which resembles an artist’s palette surrounding the mixing area. The crayon shaped pointer, which normally points to a sector of the wheel, will be repositioned to point to the mixer. Now the mixed color will be used for any coloring performed in the drawing area. To deselect the mixed color, click anywhere on the color wheel. The mixer retains the mixed color so that it can be reselected at any time. To mix two different colors, clear the mixer by clicking on the rag at the edge of the mixer before repeating the steps described above.

It is also possible to mix more than two colors. Each time a color is applied to the mixer recess the mixed color is updated. Because Shapari uses only 256 colors, the results of such multi-color mixing are not always fruitful. Accurate pair-wise mixes are guaranteed for colors that are adjacent on the color wheel (radially or circumferentially). Mixing black or white with any color on the wheel will also produce an accurate mix. These pair-wise mixes, plus the 38 colors on the wheel and a few extra shades of gray account for 178 of the 256 available colors. It may be better to think of the mixer as an intuitive way to access these colors, rather than as an arbitrary color mixer.


Anyone who has dealt with young artists knows how much they love to mix paints. The mixer provides a rough computer equivalent to this activity. Monitor color mixtures produce different results than paint pigment mixtures, but the color wheel itself provides a framework for understanding them.

Creating Patterns from Shapes


Displaying and coloring shapes are all well an good, but things don’t really get interesting until you start using the shape manipulation buttons which appear to the right of the drawing area. Clicking a shape manipulation button replaces the contents of the drawing area with one or more altered “copies” of the same. At level 1, the “copies” are simply shrunken (scaled) versions of the original. Level 2 introduces copies mirrored about vertical and horizontal (reflections) and copies that are compressed in the vertical or horizontal direction (asymmetric scaling). Level 3 adds rotated copies and copies which have been skewed (sheared). Finally, level 4 and 5 manipulations can include any combination of scaling, reflection, rotation and shear. Levels 4 and 5 also introduce manipulators that contain overlapping or partially overlapping copies.

Each button is labeled with a pictorial representation of the manipulation it performs. The pictorials show what the result would be if the button’s manipulation were applied to the notched square that appears in a recessed frame above the two columns of manipulation buttons. Owing to the nature of the manipulations, knowing what the button does to the notched square enables one to surmise what it will do to the current drawing. At first you may find it difficult to visualize what the result of a particular manipulation will be. Particular attention must be paid to the position of the notch in each “copy” depicted in the pictorial. This is especially important in the case of overlapping copies. The fact that manipulations apply to the current drawing as a whole, rather than to each shape individually can present a bit of a conceptual hurdle. The best way to get comfortable with the manipulations is to play with them.

When operating at level 1, 2 or 3, all of the shape manipulator buttons available at the given level appear on the screen simultaneously. At levels 4 and 5, the buttons are grouped into pages based on the number of “copies” produced. Only one page is visible at a time. Each page has a corresponding numbered tab to its right. To select a page, click on its tab or press a # key, where # ranges from 1-6.

The circular drawing area is surrounded by four corner buttons that work with the shape manipulations as described below.

Undo – The undo button appearing in the lower right corner reverses the effect of the last shape manipulation applied to the drawing. This button supports multi-level undo. In other words, a succession of shape manipulations can be reversed one at a time by repeatedly clicking the undo button.

Iterate – The iterate button, appearing in the upper right corner, repeatedly applies the currently selected shape manipulation (the one connected to the reference notched square by dotted lines). This repetition continues until either the drawing stops changing or the successive manipulations lead back to the original drawing (the one appearing in the drawing area when the iterate button was clicked). Surprisingly one of these eventualities almost always occurs quite quickly. In spite of this, it is possible to end the repetition prematurely by clicking the iterate button again. As a reminder of this feature the iterate button displays the image of a stop sign while repetition is in progress.

Review – The review button, appearing in the upper left corner, allows you to review the sequence of drawings leading up to the current drawing. This tends to be of particular interest after using the iterate button to perform a sequence of manipulations. When the review button is clicked, miniature versions of recent drawings are displayed in a spiral arrangement, with the current drawing at the center. The spiral is surrounded by a new set of corner buttons that can be used to control the review. Their operation is described further below under the heading “Reviewing Shape History”.

Clear – The clear button, appearing in the lower left corner, removes all shapes from the drawing window, leaving only the blank background.


Even the most advanced users may find it useful to start at level 1 and progress through level 4 while exploring the shape manipulations (level 5 is taken up later in the section entitled “Color Mapping”). The patterns that can be created get more interesting as you move to the higher levels, but each level offers some interesting, perhaps unexpected, possibilities. Many of these possibilities are achieved simply by repeatedly applying a single manipulator (using the iterate button). Another fruitful technique is alternating manipulations and coloring. There is no particular goal to this activity other than the exploration of a vast pattern space. The following section “Going on a Shape Safari” describes a goal directed activity based on the same shape manipulations. Levels 4 and 5 are open-ended in that they include the ability to define custom shape manipulations (see Customizing Shape Manipulations).

Mathematicians refer to the repeated shape manipulations available within Shapari are referred to as Affine Iterated Function Systems (or Affine IFS for short). Many of the patterns they produce are classified as Fractals. A wonderful introduction to this area of mathematics is the book Fractals Everywhere by Michael F. Barnsley, published by Academic Press, 1993 (second edition).

The Shape Matching Game


To challenge your visualization skills Shapari includes a shape matching game. The basic idea is very simple. The computer picks a shape, performs one or more manipulations and shows you the resulting shape or shapes. Your objective then is to produce the same shape(s). As you generate your shapes, those produced by the computer remain overlaid on the display so that you can always see your target. Shape color is unimportant when evaluating a match.

The controls for this game appear directly below the drawing area. They are loosely built around the metaphor of a “Shape Safari”. The idea is to take your camera and follow the shape footprints until you snap a picture of the intended quarry. The number of footprints displayed represents the number of shape manipulation steps the computer will perform. This number is easily adjusted by dragging the “shape album” that appears to the left of the footprints to reveal more or less footprints.

In keeping with the metaphor, you start a shape safari by clicking on the icon that resembles a camera case. Doing so reveals a camera icon and displays the first target shape(s) in the drawing area. By default, the first target results from selecting a shape and performing a single manipulation. Once you successfully match the first target, the camera advances to cover the first foot print and the computer applies another manipulation for you to match. Play proceeds in this manner until all footprints have been followed. At this point you have succeeded in your quest, a snap shot of the final target shape is placed in the “shape album” and the camera is returned to its bag, ready to begin the next safari. Each successful safari is also followed by a brief visual celebration (you’ll have to try it to see it). You also garner points for each successful match. The number of points depends roughly on the difficulty of the match.

For a greater challenge you can let the computer apply two or more manipulations at a time, revealing only the aggregate outcome. To control this feature click on the foot print corresponding to the first target you want revealed. For example, to have the computer perform two manipulations at a time, click on the second footprint. Every other footprint will be grayed to indicate that the corresponding shapes will not be revealed. The safari settings, including the number of footsteps and which are revealed, can’t be changed while a safari is in progress. The current safari can, however, be abandoned at any time by either clicking the camera or clicking the Clear corner button twice.

Two can play the shape matching game. Players alternately take on the role of making up target shapes, rather than letting the computer do it. To make a target, follow these steps.

  1. Set the game controls for an agreed upon number of steps and reveal interval
  2. Clear any pattern from the drawing area
  3. Draw a shape by clicking one of the shape drawing buttons
  4. Perform the requisite number of shape manipulations (excess manipulations will be ignored when the target is produced)
  5. Click the “Match This!” button that appears just to the right of the game controls. This causes the first target to be revealed. Note that this button is not enabled until the requisite number of manipulations has been performed.

Of course the other player should not be looking while the target is being composed. It is also possible to play some tricks that the computer doesn’t play when composing a target yourself. For example, a target shape can be made to disappear by coloring with the background color, or a hole within the target pattern may be colored in. These actions do not add to the safari step count. If allowed they can make matching much more difficult. The players should agree ahead of time whether and to what extent coloring is allowed. To keep the game honest, the player who composed the target should be prepared to reproduce it should his opponent be unable to do so.


The shape matching game offers a wide range of difficulties, even within a single program level. As long as the controls are set to reveal each step the game is relatively easy, although a bit of practice certainly helps. As you start skipping (not revealing) steps the game quickly becomes more difficult.

When trying to match a target, the ability to undo shape manipulations (using the undo corner button) often comes in handy. Undo behaves slightly differently when a game is in-progress. When a multi-step game is in-progress, you can only undo back to the last intermediate target match. This prevents inadvertently loosing ground in your quest. In spite of this undo restriction you can always start over by clicking the clear corner button or a shape drawing button.

One final note on shape target matching, you do not necessarily have to perform the same sequence of shape manipulations that the computer used to achieve a match. In fact you may even find some cases in which you can achieve a match using less manipulation steps than the computer did.

Reviewing Shape History


When you create a pattern using a sequence of shape manipulations, it is often interesting to review how the pattern developed. By clicking the review corner button (upper left of drawing area) you can simultaneously display the previous twelve drawing steps along with current drawing. The drawings are miniaturized to fit on the screen. The current drawing appears near the center of the screen, with the previous drawings arranged in a spiral around it. Moving counter clockwise around the spiral corresponds to moving backward through the drawing sequence.

Shapari stores up to 50 previous drawings, although only twelve can be viewed at a time. You can access drawings other than those currently displayed using the navigation buttons appearing in the upper left and right corners. The button labeled with a left facing “Reverse” arrow moves back in time through the sequence of drawings, rotating those already displayed clockwise to make room. The button labeled with a right facing “Forward” arrow moves in the opposite direction through the sequence. Note that when the review window is initially invoked, the forward button is disabled since the most recent drawing is already visible. As a navigation short cut you can also click on any of the twelve small drawings, causing the sequence to be repositioned with the selected drawing appearing in the center of the review display. You can also use the keyboard navigation keys; left arrow, right arrow, PgUp, PgDn, Home and End to move through the drawing sequence.

While the review display is visible, all operations that alter the current drawing (shape buttons, coloring and shape manipulations) are disabled. To end the review display and hence reactivate these operations, click the OK (check-mark) or Cancel (X-mark) buttons which appear in the lower left and lower right corners, respectively. The cancel button will end the review, restoring the drawing that appeared when the review began. The OK button will also end the review, but will make the drawing that appears in the center of the review the current drawing. Hence review navigation can be used in combination with the OK button to backup to any point in the drawing sequence.


When you review the results of iterating a shape manipulation the results may be somewhat different than expected. Often the drawing sequence will appear to have converged (reached its final form) several drawings before the current one. This is an artifact of the limited resolution of the small review drawings. If you view each of the drawings full size (using the review navigation an OK buttons) the differences between successive drawings will be apparent.

Each shape manipulation performed adds to the drawing sequence. Coloring operations also add to the sequence, but a succession of coloring operations, without intervening shape manipulations, adds only one drawing to the sequence. The next drawing in the sequence will show the cumulative effect of all the coloring operations.

When you step back in the drawing sequence using review navigation and the OK button, the entire sequence is preserved. This allows you to invoke the review again and return to the most recent drawing. However, once you modify a drawing in the sequence, the drawings that previously branched off from it are discarded. The program does not store multiple branches.

Saving Work in the Gallery


You can save any drawing you produce using Shapari in the “Gallery”. The gallery provides simple drag and drop storage. Separate storage is provided for each user name that has been entered via the Name and Level dialog (described earlier). There are no filenames to enter or remember.

To get to the gallery, click the left-most round button along the bottom of the main Shapari window. The full screen gallery window replaces the main window. Most of the gallery window is devoted to round frames that can hold your drawings. To the left of these frames are icons representing several places you can drag drawings to and from. To the right are a series of buttons that allow you to adjust your view of the gallery.

Whenever you enter the gallery, the upper left corner contains a miniature representation of the main window with its current drawing. To save the current drawing, simply drag it to any unoccupied round frame. Each named user can store up to 144 drawings in this manner. The view buttons along the right side of the screen control how many of these drawings are visible at once. The choices are 1, 3 x 3 = 9, 6 x 6 = 36 and 12 x 12 = 144. The more drawings displayed, the smaller each individual drawing appears. Each view button causes the program to display a view of the gallery showing the indicated number of drawings. The four possible views are nested. Each view contains all the smaller (less drawings) views. Within a given view, the smaller views are indicated by rectangles that are color coded to match the view buttons. Each colored rectangle shows exactly which drawings will be visible if the correspondingly colored view button is clicked.

Each view, other than the 12 by 12 view, shows only a portion of the gallery at a time. The arrow shaped buttons appearing along the perimeter of the view area can be used to move the view, periscope style, to another portion of the gallery. The keyboard arrows, on the other hand, can be used to move the innermost (single drawing view), dragging the other views along as necessary to keep the views nested. The innermost view can also be repositioned by clicking on any visible drawing.

Drawings that have previously been saved in the gallery can be recalled for further modification in the main window. To recall a drawing, drag it from its gallery frame to the miniature main window. When you return to the main window a full size copy of the drawing will be there. The original will remain in the gallery.

The gallery can also be rearranged by dragging any drawing from its present location to another location. If the new location is unoccupied the drawing simply moves there. If it is occupied then the two drawings trade places. To remove a drawing from the gallery, drag it to the recycling bin appearing at the bottom left.

Changes to the gallery are not saved until you click the round OK button (check mark) which appears near the bottom right corner. Clicking the OK button saves all changes and returns to the main window. To cancel all changes made since entering the gallery, click the Cancel (X mark) button instead.

The gallery also serves as a bridge to the system clipboard and to the printer. The system clipboard allows text and graphics to move from one program to another. Shapari can export drawings to other programs via the clipboard. Dragging a drawing to the clipboard icon at the left edge of the gallery places a copy on the system clipboard. Other programs can then use the Shapari drawing (typically by pasting it into a document).

To print a drawing, drag it to the printer icon that also appears along the left edge of the gallery. While the drawing is being printed, a flashing image of it appears on top of the printer icon. Printing may be canceled by clicking the Abort button that appears just below the printer icon. This may result in a partial printing depending on the how far the process has progressed when you click the abort button. Also appearing below the printer icon is a printer setup button. By clicking on this button you can access standard printer selection and setup dialogs.

If you enter the gallery and find another user’s work displayed, you may wish to change the current user name via the name and level dialog. You can access this dialog directly from the gallery by clicking a round button appearing in the lower right corner (the one bearing a staircase icon). If you change the current user name, the previous user’s gallery collection will be closed and the new user’s gallery collection will be opened. While the collection is being opened, brown dots may briefly appear in the drawing frames as placeholders until actual drawings are loaded.


Young users love to save their creations. The Shapari gallery provides an easy way for them to do so. The gallery is also easy on system resources, creating only one compressed file per user.

To view a gallery collection of sample drawings select the user name “Sample” in the name and level dialog.

Overlaying Shapes


Earlier, pattern creation from a single shape was described. When operating at levels 4 and 5 Shapari lets you add shapes to existing drawings and hence create drawings from more than one shape. The mechanism for doing this is the shape overlay. To overlay a shape, click the “add overlay” button that appears in place of the last shape button at levels 4 and 5. Pressing this button displays a dotted, notched square in the drawing area. Think of this square as a home for a shape. When you subsequently click a shape button, the selected shape will be placed in this home. However, before doing this you can manipulate the home (altering and/or copying it) just as you would an actual shape. When overlays (or homes) are on screen, the manipulators alter them without affecting the underlying drawing.

When the shape homes are in the desired position they can be filled in with actual shapes. Each time you click a shape button, the active home (denoted by a dark dot at the tip of its notch) will be occupied by the selected shape. To activate a particular home, click the dot at its notch. You can also cycle through the homes using the tab key. To remove the active home, without introducing a shape, click the “remove overlay” button, which replaces the “add overlay” button when a home is present.

If, by repeated application of manipulators, a shape home becomes too small, it will be considered uninhabitable and will become part of the underlying drawing. If this happens you can undo the last manipulation to restore the home if you wish.

Shapari will not use overlays in the course of generating patterns to be matched, nor will it allow you to convert a pattern constructed using overlays into a target for another player to match.


Overlays open up a whole range of possibilities. They are particularly handy for adding finishing touches, like eyes. It’s best not to get too carried away, however. Positioning shapes with overlays is a bit of a challenge (along the lines of the matching game). For a high degree of explicit control your better off with a drawing program. Remember, brainstorming, not deliberate design, is Shapari’s forte.

Customizing Shape Manipulators


At levels 4 and 5, you can modify existing shape manipulators and/or create your own. To modify an existing manipulator, select the manipulator button then click the Edit button appearing at the top right corner of the manipulator palette. Alternatively, you can right click a manipulator button to display a context menu that includes an Edit option.

To create a new shape manipulator, either click the New button at the top left corner of the manipulator palette or right click anywhere on the palette and choose New from the context menu that appears.

In addition to the Edit and New options, the manipulator palette context menu offers the following choices:

Cancel – Closes the context menu without taking any action.

Cut – Removes the selected shape manipulator from the page, saving it on an internal scratch pad

Copy – Copies the selected shape manipulator to the internal scratch pad

Paste – Adds the shape manipulator residing on the internal scratch pad to the current page. If the current page is full, another page is created.

Duplicate – Adds a copy of the selected shape manipulator to the current page (or new page if full).

Move – Repositions the selected shape manipulator on the page by swapping it with an adjacent shape manipulator.

Save Changes – Saves the customized collection of manipulators so that it will automatically be loaded the next time the user starts the program.

Undo Changes – Discards all manipulator changes that were made subsequent to the last Save.

Recall Original – Loads the original Shapari shape manipulators. When you invoke this choice you will be asked whether you want the program to retain your custom manipulators for possible future recall. If you answer no, your custom manipulators will be permanently deleted.

Recall Custom – Loads previously saved custom shape manipulators

Each user can have his/her own custom manipulator collection. The program automatically saves manipulator collections by user name. The program also remembers whether a given user was last using the custom or original collection. Users can exchange custom manipulators by copying, switching users and pasting. In other words, the internal scratch pad is not disturbed when switching users.

When you invoke the shape manipulator editor, an enlarged manipulator diagram appears in the center of the screen. Surrounding the diagram are four editor control buttons whose use is discussed below. To the left of the diagram is a dialog that allows precise manipulator specification. More often, however, the mouse will be used to directly alter the manipulator diagram. Operation of the editor is similar to that of a typical drawing program which lets you draw, move, resize, rotate and skew objects. Here, however, the set of objects is highly constrained, consisting of notched squares, rectangles and parallelograms, representing “copies” of the original notched square.

To add a copy to the shape manipulator under edit, click the plus button that appears in the upper left corner. A new, full sized copy will appear, ready for alteration. To signify this readiness, the notched square has a transparent interior and has a series of handle squares around its perimeter and at its center. The new copy is said to be in the “selected” state. You can select an existing copy for alteration by simply clicking on it. In the case of overlapping copies, successive clicks cycle through the pile. To clear all selections, click any unoccupied area within the circular display area. To remove a copy from a manipulator, select it and then click the minus button that appears in the upper right corner. A manipulator can contain at most 12 copies.

Copies can be altered by dragging handles. First a handle must be activated. To activate a handle, left click one of the handle squares. A menu of motion choices appears. The particular choices depend on whether you have selected a center, corner or side square. The menu will include some or all of the following choices:

Tack – The tack holds the associated point at its current location. A second handle may be activated to move other points relative to the tacked point.

Single Arrow – The single arrow allows the associated point to be moved in the directions indicated.

Double Arrow – The double arrow allows full two-dimensional motion

Curved Arrow – The curved arrow allows the associated point to be rotated about the tack point. The tack must be activated before the curved arrow can be activated.

Curved Arrow & Axis – The curved arrow & axis combination allows a point to be rotated about an axis lying in the display plane and passing through the tack (in contrast with the curved arrow which uses an axis perpendicular to the display plane). As before the tack must be activated first.

With the menu of motion choices displayed, move the mouse pointer over the desired choice and left click to activate it. Click anywhere other than the menu to deactivate it without choosing a motion

Once a handle has been activated (but not tacked) you can drag it to alter the selected copy as desired. To change the motion of the active handle, click it without dragging to redisplay the menu of choices. If you select no choice, the handle will be deactivated. The motion handle will also be deactivated automatically if you activate a motion handle at a different point. There can only be one tack and one motion active at a time.

In addition to the handles discussed above, there is a special handle associated with the notch that establishes a copy’s orientation. Within the notch is a triangle. Pressing the left mouse button when positioned over this triangle activates the notch handle as indicated by the appearance of a bent arrow. With the mouse button still down, you can drag the notch around the perimeter of the copy without otherwise altering its shape. The notch handle serves as a handy shortcut for many copy alterations. Other active handles do not affect notch handle operation.

When a motion handle (other than the notch handle) is activated, its position is reported in boxes that appear to the left of the circular edit area. If a point has been tacked down, the position of the motion handle relative to the tack is also reported. The coordinate system used for these position values is displayed in the circular edit area. The origin is at the lower left, with a horizontal x-axis increasing to the right and a vertical y-axis increasing upwards. Along the x and y-axes are scales ranging from 0 to 1. Relative to this coordinate system the original reference square is a unit square with corners at (0, 0), (0, 1), (1, 0) and (1, 1). Each scale includes a series of shaded bands, each bearing a different set of sub-divisions. Moving from the middle toward the outer edge of the edit circle you encounter bands that divide the scale into 1, 6, 8 and 10, equal parts. By clicking on a band you can activate a corresponding set of grid points to help gauge the movement of handles.

As you drag a handle, the position values displayed at the left are automatically updated. This makes it possible to alter copies with some degree of precision. For even more precision, you can enter values directly. Values so entered do not take effect until you click the Apply button that appears below the value entry boxes. Once the Apply button is clicked the diagram is updated to reflect the changes. If instead of clicking the Apply button, you click the Reset button, the box entries return to their previous values, i.e. those currently reflected in the diagram. Note that the six values you can enter are not fully independent, hence editing one value may affect others. This happens automatically. Also note that the top two values are shown only when a motion handle has been activated. While the bottom four are shown only when both a motion handle and a tack have been activated.

Above the value entry boxes (near the upper left corner of the screen) are three tabs labeled Handles, Corners and Matrix. The handles tab is associated with the handle position values just described. The other two tabs provide access to alternative numerical descriptions of a copy. As with the handle position values, the values displayed while either the Corners or Matrix representation is active update automatically as you alter the selected copy using the mouse and can also be altered directly via the keyboard. The meaning of Corners and Matrix values is described below.

Corners – This representation is based on the constraint that the “copies” of a square under Shapari are always parallelograms (squares and rectangles being considered special parallelograms). Three corner points uniquely specify a parallelogram. Hence, you can specify the parallelogram representing a copy of the original notched square by entering position values for three of its corners. Specifically you can enter final locations for the notched square corners that were originally located at (0, 0), (1, 0) and (0, 1). In contrast with the Handles values, the six Corners values are completely independent of one another.

Matrix – The matrix equation displayed when the Matrix tab is selected provides a compact representation of the mapping from original to copy. The matrix equation corresponds to the following pair of simultaneous equations which map the point (x, y) to the new point (x’, y’).

x’ = M11 x + M12 y + B1

y’ = M21 x + M22 y + B2

Although, not as intuitive as the previous representations, the matrix representation is the method preferred by textbooks which cover transformational geometry. As with the Corners representation, the six Matrix values are all independent.

A very effective technique for defining copies is to shape them roughly using the mouse and then fine tune the definition by editing the numerical values. Don’t forget to click the apply button to effect the changes.

Shapari allows you to simultaneously alter a group of copies. First the group must be selected. There are two ways of doing this: (1) drag a box around the copies or (2) hold down the Shift key while clicking on the copies one at a time. Clicking on a copy while holding the shift key actually toggles its membership in the group. Hence shift-clicking can be used to add or remove copies from a group. These methods are fairly typical of object drawing programs. Once a group has been selected a bounding box (rectangle) with handles surrounds it. The bounding box can be altered in the same ways a single copy can, i.e. by using the handles or by entering numerical values. As the bounding box is altered, so are the copies inside it.

For convenience you can click in the circular edit area with the right mouse button to display a context menu. This menu offers the following options:

Cancel – Closes the context menu without taking any action.

Undo action – Reverses the effect of the last editing action, where the action is Add, Delete, Duplicate, Move or Apply.

Add – Like the plus corner button, adds a new copy to the diagram.

Delete – Like the minus corner button, removes the selected copy or group of copies from the diagram.

Duplicate – Adds a copy or group of copies identical to that currently selected. The copies sit directly on top of the originals until you move them.

To end an editing session click either the OK (check mark) or Cancel (X-mark) corner button. When the OK button is selected, the manipulator collection is updated to include the new or altered manipulator. Recall that manipulators are grouped onto pages based on the number of copies they include. Hence editing a manipulator may change its location within the collection (if copies are added or removed). When the cancel button is selected, all editing changes are discarded, leaving the manipulator collection unaltered.


As mentioned earlier, certain shape manipulators, when applied repeatedly, yield fractal patterns. With the ability to customize shape manipulators, you can explore the relationship between manipulators and the fractals they produce. With some practice it is possible to work backwards from a fractal pattern (perhaps one observed in the natural environment) to the manipulator which produces it.

Another use of shape manipulator customization is the ability to tailor the matching game, perhaps making it more difficult or emphasizing some particular facet of shape discrimination. The editor itself can be used as a tool for exploring geometric transformations. In summary, shape manipulator customization provides relatively advanced users an opportunity for open-ended exploration.

A word of caution when specifying copies by entering numeric values; it is possible to enter values the stretch a copy beyond the edit area, or position it completely outside the edit area. In the latter case, Shapari will refuse to apply the values, instead issuing a warning. Generally speaking, copies that stretch beyond the edit area, while permitted, are not useful for pattern creation.

Color Mapping


The shape manipulators described thus far can be viewed as mappings in space. A shape manipulator maps each point in the original drawing to one or more points (one per copy) in the final drawing. At level 5, Shapari adds a simultaneous color mapping whereby the color of a point in the original drawing may be mapped to a different color in each copy. The color mapping is defined by a color cycle and a color step (as will be explained shortly).

At level 5, the shape matching game (safari) controls at the bottom of the screen are replaced by a row of color cycles. There are 10 color cycles arranged in two rows of 5. Click on the arrow shaped buttons to the left of the color cycles to select the desired row. Or use the keyboard arrow keys.

Each cycle contains a different number of colors. To activate a particular cycle, click the raised button at its center or use the keyboard arrow keys to move the selection up, down, right or left. Four circulation arrows around its perimeter denote the active cycle. Activating a color cycle has no immediate effect on the current drawing. Instead the cycle is used in conjunction with the shape manipulators to define a color mapping as described below.

At level 5 the shape manipulator diagrams include copies that are labeled with color steps values. These represent clockwise steps around the active color cycle. When a copy having an associated color step, N, is produced, each color in the original is located on the color cycle. Each is then replaced by the color appearing N positions clockwise around the cycle. Colors that appear in the original drawing, but not on the active color cycle are not mapped. Furthermore, the background color is never mapped.

If the color step associated with a copy is 0 then the copy retains the original colors, i.e. no color mapping takes place. Such copies appear unlabeled in the shape manipulator diagrams. Copies with non-zero color steps are not only labeled with the step value but also shaded (the greater the step value the lighter) to emphasize their behavior. When you customize a shape manipulator at level 5 the editor is augmented with a color step control that can be used to assign a color step value to selected copies.

Color mapping can be disabled for all manipulators by selecting the first cycle in the first row of cycles (the one with no color). Manipulator behavior is then no different than at level 4.

You can customize the color cycles with your own color combinations. To do this:

  1. Choose the color you want to include in the cycle using the color wheel or color mixer.
  2. Move the mouse pointer over the color cycle sector that you wish to change (the pointer becomes a crayon)
  3. Click with the left mouse button to deposit the color in the sector.

5. Repeat steps 2-4 for all sectors you wish to color.

When you want to use the customized cycle activate it by clicking the button at its center. To save your custom color cycles, right click on the color cycle page (anywhere except where the crayon pointer is displayed) to reveal a context menu. The menu choices include:

Cancel – Closes the context menu without taking any action.

Copy Cycle # – Copies the indicated color cycle to an internal scratch pad.

Paste Cycle – Updates to colors in a cycle with those on the internal scratch pad. This allows users to share color cycles.

Save Cycle # Changes – Saves the colors currently appearing on the indicated cycle so that they will automatically be loaded the next time the user starts the program.

Undo Cycle # Changes – Discards all color changes that have been made to the indicated cycle since the last Save.

Recall Cycle # Original – Loads the colors that originally appeared on the indicated color cycle (program defaults).

Save All Cycles – Saves the colors currently appearing on all 10 color cycles so that they will automatically be loaded the next time the user starts the program.

Undo All Changes – Discards all color changes (to all cycles) since the last Save.

Recall All Originals – Recalls the original colors of all 10 color cycles. When you invoke this choice you will be asked whether you want the program to retain your custom colors for possible future recall. If you answer no, your custom colors will be permanently deleted.

Recall Custom – Loads all previously saved custom colors.

As with custom shape manipulators, each named user has a private collection of custom color cycles.

The above paragraphs define the basic color mapping capability. In addition there are several fine points to be considered:

Right clicking the mouse while it is positioned over a color cycle sector (crayon pointer displayed) has the opposite effect to left clicking. In other words, the color appearing in the sector becomes the current color for drawing or filling shapes in the drawing window. This provides a convenient way to ensure that a color you use in the drawing window will be mapped (recall that only colors appearing on the cycle are mapped).

Recall that the iterate button (upper right of drawing window) applies a manipulator repeatedly until the drawing stops changing. When the manipulator effects a color mapping, the drawing may never stop changing, hence the repetition will continue until explicitly stopped (by clicking the upper right button again). The indefinite repetition of manipulators with color mappings can be used to achieve some interesting visual effects. You can control the speed of the repetition from the keyboard. Pressing the plus (+) key increases the repetition rate and pressing the minus (-) key decreases it.

When color mapping is enabled and you apply a shape manipulator that produces multiple overlapping copies, the order in which the copies are produced affects the outcome. For consistency, copies are always produced in order of increasing color step. Copies with the same color step are produced in the order they were last touched in the manipulator editor.


At first the color mapping capability may seem complicated and somewhat fanciful. Keep in mind that Shapari is intended to stretch the brain the way abstract systems often do. Aside from the fanciful uses, color mapping effectively color tags the individual copies produced by a manipulator, providing insight into exactly what is going on.