## On the Line

###### Posted on 12 March 2015

Playing With Shapes Brainwright

In this game, players are given sixty different pattern cards, each having a unique design on them. I created the designs on each of these cards by using four shape pieces. Once a player selects one of the pattern cards they take four of the shape pieces and begin constructing the design.The pattern cards bring a special dynamic to both play and the emphasis of algorithmic thinking. As artistic elements in themselves, they present some aesthetic value to the players. Children often picked from the deck ones that looked “pretty” or “cool” to them. Beyond the aesthetic value, each pattern card holds a rule based algorithmic solution to constructing it. The cards can be categorized into three classifications based on the number of rules each card uses.

The pattern cards for this game were generated using a shape grammar system that followed one, two or three design rules. Cards that used one rule are using the rotational transformation schema x → x + t(x). The initial shape piece is duplicated recursively and rotated around a fixed pivot point resulting in a series of similar designs. Although each of these one-rule pattern cards visually look different it is important to note that they each have a shared schema. The transformation “t” uses the rotation transformation carried out recursively. Pattern cards that use two rules rely heavily on reflection. The two-rule pattern cards are combining rules so that once the first rule is applied a second rule is applied to the same base shape. The first rule applied uses the schema x → x + t(x); the solution then is completely forgotten as a second rule is applied on top of the existing composition. The same schema x → x + t(x) is applied to the shape variable building up the complexity of the final composition. The two rules are using the same schema applied differently on each computation pass. The transformation “t”, in some of these cards use the reflection transformation or rotational transformation at 180 degrees (depending on how you see it). This could be substituted with either a translation or rotational transformation at a different angle to yield alternative compositions. Pattern cards generated by the usage of three rules might be the most generous of the entire set. While the rules of creation might be clear when designs are restricted to one or two rules, the patterns generated by three different are the most ambiguous.

The transformation “t” in cards using three ruels might take the form of any of the three isometry transformations. The pattern cards that use three rules to create the composition might use the rules at random but interesting enough they create some of the same emerged shapes seen in the pattern cards that use one and two rules. Although the descriptions of the shape cards show how compositions can be organized by the generating rule, the pattern cards could also be organized by what our eyes see. Classifications of families might be created in these pattern cards through the likeness of emerged shapes. Some compositions produce emerged triangles and squares, while others produce pentagons and rhombus shapes. Additionally, there is the overall outline of the compositions that produce octagons, crosses, and pinwheels. The artist is free to use whatever the eyes see.

Embedding shapes upon each other is essential to play this game; however, this was not apparent to all players in the study. Some players looked confused and expressed that the task was impossible with just four shape pieces. In testing the game out, some children were also seen looking through the pile of game pieces for shapes that matched the discreet geometries seen on the pattern card. *“I need a triangle piece,” *one child proclaimed in frustration as they looked through the pile of identical shape pieces. Embedding is a critical concept to grasp in the mastery of visual calculation. These cards allow players to transform the shapes on the cards in ways that would not be possible using a combinatorial based system. Furthermore due to the “flatness” of the line quality, new shapes can emerge that completely overpower the original base shapes. The original shapes begin to disappear to the eye as new shapes emerge. This of course does not rule out combinatorial play. Connecting pieces as units is often the first step of discovery for children. The child will begin to see new forms appear through playing and manipulating shape cards.

On the Line * *is very effective in presenting the system of shape grammars and visual calculation. The way the game pulls the players into a way of seeing the new shapes and prompts them to forget the base shape is exactly what shape grammars is all about! In this type of calculation you do not hold on to the identity of the starting variables; you are allowed to forget them and calculate with new emerged shapes.