I have fun playing around with symmetries and using them to create images no one has ever seen before.
Currently I am exploring multiple reflections at lines and inversions in circles creating tilings of hyperbolic, elliptic and Euklidic space. Additional reflecting elements make that the tilings become fractals. Some of the tilings are made of tilings that resemble themselves in a recursive way. For more information see my contribution "Fractal Images from Multiple Inversion in Circles" to this conference.
It is difficult to show the structure of these tilings in a still image. You better do your own experiments with the browser apps you can find at http://geometricolor.ch.
This is a quincuncinal projection of a decoration of a sphere with octahedral symmetry.
It results from multiple reflection at two straight lines and inversions in two circles. The two lines and each of the two circles define a elliptic triangle. This three elements alone would create a tiling of the sphere with octahedral symmetry. All four elements together too generate such a decoration. But now it contains distorted stereographic projections of itself. Thus an infinite recursion arises and there are copies of the image inside copies of the image inside the image and so on.
You find the browser app that can create this image at "http://geometricolor.ch/circleInTriangle.html". Check it out yourself !
Multiple reflection at two straight lines and inversions in two circles create the structure of this image. The lines and circles intersect like a chain and delimit two quadrilaterals. Their images make up a tiling of the plane. A photo is finally mapped onto the structure similarly as in a kaleidoscope to create a visible image.
A fractal line similar to a Koch snowflake separates two regions. The inside shown here in mainly red and olive green colours is filled by images of one quadrilateral. Images of the other quadrilateral fill the surrounding area in light blue and white colours.
I have published the browser app I used for creating this image at "http://geometricolor.ch/quadrilateral.html". Try it out yourself !