My Goals:
My goal is to get children to explore with the tool and create a variety of original artworks that they would want to save or even print out. While doing so, I also want them to get excited about math (or possibly even grow an appreciation for it), and realize that it can create appealing art simply by altering some numbers or code using a familiar control interface (the game controller).
My interest lies in abstract/organic generative art and I would like the created images to have those characteristics, but because I have to keep in mind that it must appeal to young children, I plan on incorporating vibrant colors and simple shapes (circles, triangle, square, stars? etc).
My other goal is the explore a child's developmental process, which according to Piaget grows through reflection abstraction, empirical abstraction, and cognitive stage (detailed definition at the bottom of this post).
The Graphic Tool Interface:
I would like to exploring several fractal equations including spirals (Archimedean, Cornu, Fibonacci, Loxodrome), tree, and the Mandelbrot.
So far, I am working on the spiral:
- When the graphic tool first starts up and the user clicks on the interface to draw, a small spiral will generate from that coordinate. The user will be able to change the direction and create new spirals using the joystick. This initial layer functions as the wire-frame view, which appears to be structured but give a straightforward image of the fractals that they've created.
- using different buttons on the controller, the user will be able to transform their visual by applying color filters, altering values in the equation (which could make drastic or even random changes to the pattern and shape), or making changes in the code so that the command changes while keeping the same values (translate(), popMatrix(), rotate(), bezier()... etc.).
first layer:

after one type of basic "color filter":

The Developmental Process
child performs an action which has an effect on or organizes objects, and the child is able to note the characteristics of the action and its effects
“reflecting abstraction” -through repeated actions, with variations or in different contexts, child is able to differentiate and integrate its elements and effects
“empirical abstraction” -child is able to identify the properties of objects by the way different kinds of action affect them
forming a new “cognitive stage” -by repeating this process across a wide range of objects and actions, child establishes a new level of knowledge and insight
once the child has constructed these new kinds of knowledge, he or she starts to use them to create still more complex objects and to carry out still more complex actions