# Peter Stampfli

Avenches, Switzerland

I like the self-similar shapes of crystals and ferns, the geometric art of M. C. Escher as well as the concrete art of Max Bill and Verena Loewensberg.

I love playing around with symmetries, using them to create images no one has ever seen before. With multiple reflections at lines and inversions in circles, I create tilings and fractals in hyperbolic, elliptic and Euklidic space. You can explore that for yourself using my browser apps, which are on the site geometricolor.ch.

Currently, I am developing ‘KaleidoBuilder’, a browser app that makes every kaleidoscope you could imagine. Actually, this app is also a fun way to explore group theory and geometry.

Hyperbolic serendipity
15 x 15 cm
Digital image/print
2020

This image results from debugging the forthcoming ‘kaleidoBuilder’ browser app. The circles at the bottom define a Poincaré disc representation of hyperbolic space, where they are straight lines. The white circle inverts only points lying inside, and the black circles invert points lying outside. The color of a pixel results from repeating these mappings on its position until they all stop. The circle that did the last inversion gives the pixel’s color. I get an irregular tiling of hyperbolic space as the circles intersect at angles that are not integer fractions of 180 degrees. The outside of the disc is an inverted image of its inside. I bleached its colors and converted them to black and white for emphasizing the inside.

Farctal doodle
15 x 15 cm
digital image/photo
2020

Haeckel’s photos of radiolarians inspired this image. It is a composition of various results from my browser app at http://geometricolor.ch/images/geometricolor/koch/koch.html. This app generalizes Koch’s snowflake. Instead of the equilateral triangle it offers polygons, star-polygons, radial lines or star like shapes as initial shape. Then, each iteration replaces each straight line by four smaller straight lines, similarly as for Koch’s snowflake. But the ratio between their lengths and the angle between the lines can now be chosen in a wide range. This gives a large variety of fractal shapes. I selected some of my results and used GIMP to transform and paste them together.