Illustration

This page's title image was generated using my Desmos model that lets you toy with filled-in Julia set approximations. Specifically you will pick a favorite complex number c=a.exp(it) and consider the dynamics of the associated quadratic monic polynomial. Here is the Desmos link:

https://www.desmos.com/calculator/8an55hvcj8

I also made one for the the associated cubic and quintic monic polynomials. Here are the links:

https://www.desmos.com/calculator/ykg8ipxryw

https://www.desmos.com/calculator/d3xyttbhas

A happy hyperbolic 9-gon

Paradoxical Hopscotch (not special)

Matryoshka Implosion

X

Hairy

S

Circle Area Approximation

Classification of actions on 6-hyperbolic spaces

Joint with

S. Balasubramanya

The proportions and shading make your brain think that the back side is much further away than the front. The back side and front side are the same size, violating the law of perspective. This creates an optical illusion: the backside seems larger because it is not smaller.

Joint with

D. Futer and M. Hagen

A spherical triangle

Joint with

D. Futer and M. Hagen

You can zoom in on the details in the Desmos model, and play around with the three parameters, where c=a.exp(it) and K is the radius of the disc whose backward iterates intersect to yield the filled-in Julia set. For that, K must be sufficiently large for the given c=a.exp(it) but many interesting patterns emerge for small K as well.

Artistic Influences:

Gonzalo Fernós Lopez

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