Our perceived world is 3-dimensional, but even though most of us have a decently functioning stereoscopic vision, our ability to grasp the possibilities that space has to offer are quite limited. We rule space using box shaped blocks (houses). This is convenient, because it is simple and makes space accessible even computationally.
We surround ourselves with endless repetitions of familiar shapes, largely ignorant of the fact that there are many other simple ways to create and explore rather exotic shapes with an alien but compelling esthetics.
The images from this page are all produced using quite simple formulas, using what are called harmonic functions.
They are related to minimal surfaces (soap films), but much more flexible.
For the mathematician, the challenge is to find out how the algebraic properties of the formula are related to the geometric properties of the corresponding shape. This is largely done by experiment, to the surprise of many who don’t think Mathematics is an experimental science.
At our fingertips we have infinite uncharted worlds to explore. We do not slaughter the natives, nor do we spend billions on super colliders or space probes.
Our discoveries are always fundamental, and useful only as a byproduct.
This sounds arrogant. In reality, it is just the belief that truly useful things have to be simple. This is our justification to explore simplicity for its own sake.