Browser apps for creating images:
kaleidoBuilder - Create kaleidoscopes by putting together inverting circles.
Generalized Koch Snowflake - Create fractal images with dihedral symmetry.
Kaleidoscope - Create periodic kaleidoscopic images in spherical, Euclidic and hyperbolic space.
Kaleidoscope with quadrilaterals - Create hyperbolic and fractal tilings using reflections at the sides of quadrilaterals.
Kaleidoscope with a circle in a triangle - Create fractal tilings using reflections at two straight lines and one or two circles.
Five circles - Create fractal tilings using reflections at two straight lines and up to three circles.
Wallpapers from waves - Create quasiperiodic and periodic wallpapers using symmetric wave packages.
fractals and quasiperiodic tilings - generate such beasts with a *.json file definition
gridmethod - using the grid method to generate quasiperiodic rhombus tilings with special decorations
twelve-fold 2 plus sqrt(3) - a kaleidoscope with quasiperiodic structure, self-similarity ratio 2 + sqrt(3)
twelve-fold 1 plus sqrt(3) - a kaleidoscope with quasiperiodic structure, smaller self-similarity ratio 1 + sqrt(3)
If you want to know more:
Presentation for the Bridges 2022 conference in Helsinki - This downloads the presentation as a pdf
"Quasiperiodic Tilings with 12-Fold Rotational Symmetry ..." - Paper on 12-fold quasiperiodic tilings.
"Ptolemy, the Regular Heptagon, and Quasiperiodic Tilings" - Paper on 7-fold quasiperiodic tilings.
"Fractal Images from Multiple Inversion in Circles" - About kaleidoscopes with more than three mirrors.
"Kaleidoscopes for Non-Euclidean Space" - A paper which explains in detail how the kaleidoscope app generates the images.
My blog - A rambling discussion about geometry and programming, including kaleidoscopes. Look at the posts of early 2018.Code repository - Has the code of the Kaleidoscope app and more.
Experimental:
quasiperiodic rhombus tiling 3-fold symmetry
Peter Stampfli, Rue de Lausanne 1, 1580 Avenches, Switzerland
pestampf@gmail.com