Plato’s allegory of the cave - a rumination on the nature of belief versus knowledge - is depicted here as a parametric surface, which remains fixed from a specific angle yet changes rapidly when viewed from others.

In our first iteration, we created a 2D surface that is projected onto a plane. While the form of the object changes, its projection remains fixed. The surface is projected from a single point via 4 lines onto a flat plane in front of it. Three parameters can be changed in this model: the projection distance, the size of the projection, and the iteration seed.

In our second iteration, we added one more dimension to what came before, and created a sphere with the projection of a cube located within it. While the original form of the cube changes rapidly when viewed from its exterior, its projection on the surface of the sphere remains constant. In addition to this, the cube also maintains its shape when viewed from the projection point inside itself using a wide angle lens. The variables of this model are derived from the overall radius of the sphere, so only the radius and the seed iteration parameters can be changed here.