Design statement
Previously, we experimented with the use of polygons to form the illusion of 3-dimensional figures. In this project, we further explored the ways in which relative shape with respect to the lens and vanishing point, and relative shading and color intensity with respect to a light source1 can create a more lifelike 3-dimensional image.
Our image is a cube composed of many smaller cubes with negative space in between. The depth of the cubes varies from a single cube to several layers of smaller cubes that compose the whole. In different images, the cubes will vary in color, with shadows painted using the complementary color of the cubes. The cubes will be painted against a colorful background.
 
Implementation
To achieve the 3-dimensional illusion, in the base case, we established a large static cube which was filled entirely solid, and with one smaller cube at each vertex and in the middle. We constructed the cube using a recursive procedure in which the base case drew a cube with an identical cube joined at each vertex. The outline structure of the base-case was defined by predetermined vertices stored in a list. We used a soft brush to stroke the outlines of the cube using a complementary color, and the three visible faces of each cube were filled in using select-polygon! on the appropriate vertices. The same procedure could be called recursively through a helper procedure, which calls it 9 times for each recurrence. For all the recursive calls in one step, the respective vertices of each sub-cube was determined by trisecting the edges of the bigger cube and finding the intersections of lines with those trisections as endpoints. There will be no more than 4 recursive calls. We painted the background with n circles and n lines that are placed diagonally using GIMP tools. Each circle was off set by a certain distance from its previous circle both horizontally and vertically, and we used recursion to achieve this. The lines were drawn using a similar algorithm. The color scheme was also based on a function of n. By varying n, we obtained different colors of circles and lines for our background. 
 

We mainly focused on building the recursions and constructing the cubes, so we gave up the idea of using fractals to create patterns on surfaces of each cube. Also, since we already had relatively colorful background, additional patterns on cube surfaces would make our image too crowded and less visually attractive.  We also did not experiment with the warm and cool colors we proposed in our first proposal, because we did not have time for that.
 
We know we have 1000 distinct images because of the variation of color and the level of recursions. The colors were derived by converting n to base 7, and the last 3 digits represent the red, green, and blue components, respectively.  We chose 7 because it is a prime number and we could identify 7 discrete integers to represent each step in color change. This method was used to determine the color of the cubes and the base color of the background. Since the cycle ended up repeating after 73, the remaining images were still distinct from the first color cycle because the maximum number of recursions plus the base case (5) is relatively prime. Thus, the second color cycle started with a different cube configuration.
 
1David Kraemer gave the idea of establishing a light source.