Risto A. Paju

Jyvaskyla, Finland
My math-art awakening took place during an undergraduate summer course of fractal geometry in 2015. Having no background in visual arts, this opened up a weird new world of expression to complement my endeavours in music and theatre. I joined the Bridges community at the 2016 conference with artworks, a short film and a short paper.

In a time where playing computer games is considered sport, and algorithms are portrayed as tools of manipulation and oppression, I want to show the power and fun in writing your own software. Math is everybody's possession, you can choose where and how to use it. As Arthur Miller put it: “Man must shape his tools lest they shape him.”
Inversion Walk
Graphics and music by Risto A. Paju
This short film is a medley of my inversion fractal demos from mid to late 2019, generated in my custom OpenGL framework. Most of the sections involve regular circle/sphere inversion, but a few other shape inversions also make appearances.

I aim to breathe new life into classical inversion fractals by playing with the base geometry. Infinite lattices, mixed shape inversions and moving geometries are featured prominently here, including the eponymous "walking" lattices. The initial sets are also varied from spheres to cubes and octahedra, in cases where they fit the inversion geometry.

For a visually fulfilling inversion fractal, the generating shapes should maintain kissing positions with each other. This presents a challenge for moving geometries. One interesting solution, featured here in both 2D and 3D variants, is a family of Steiner chains; the chains themselves are formed by circle inversion, before being used to generate the inversion fractals.