# Risto A. Paju

Artist
Jyväskylä, 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.”
Lost in the Knot
00:02:10
Graphics and music by Risto A. Paju
2022
Lissajous figures are a convenient source of smooth curves for algorithmic artists. I have used them for fixed shapes as well as paths for moving objects, and even for moving the point of view.

This film presents an inside view of the curve x = sin(2t + 0.1); y = sin(3t + 0.337); z = sin(5t). While I originally adjusted the parameters for visual harmony only, this curve turned out to be a Lissajous knot, and it inspired me to learn more about knots in general.

The braided style of the latter half is also related to Lissajous figures. Regular flat braids can be realized as 2D Lissajous curves with the third dimension as the free variable t, and the tube braid shown here is likewise based on sinusoids with phase offsets.

To show the front seat view, the camera follows the curve with t proportional to real time. The speed of propagation dl/dt is then turned into engine noise, using MIDI pitch bend commands sent to a synthesizer.