Risto A. Paju

Jyväskylä, Finland
I discovered the art of iterated function systems (IFS) in a course of fractal geometry during Summer 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 soon developed a new plotting technique for colouring IFS graphs, and presented it in a Bridges 2016 paper.

As an occasional maths and science teacher, I could always use fresh reasons why a young person should take up maths. With these pictures, I hope to make a strong case for mathematics as a culture and an art, rather than a mere tool for engineers and economists.
trig flow
Graphics and music by Risto A. Paju
This animation presents two examples of my live OpenGL demos, as used in Aino Martiskainen's stage play Pyydettiin siipiä. Both are based on functions in R^2 of the form

f(z) = z + a*sin(b*z) + c*sin(d*z')

where the sines are computed componentwise, and z' means z with its x and y components swapped. It was inspired by Pickover's Popcorn algorithm. To break up the regular lattice, I have added frequency modulation into both terms. The function parameters vary continuously over time, based on a random walk process.

The first section shows continuous iteration in time, and each frame is a successive iterate. New colour percolates in from the edges to further visualize the flow. The second part uses the same function with the same progression of parameters, but each frame is an independent IFS graph using my colour overlay method. This way, the same function can portray very different moods in the play.