I have no 3D intuition. I began to render math models using a ray-tracing software (Povray). But I needed to draw several images to get an idea of the 3D aspect of those models. Then I began to learn Blender, in order to be able to turn around my models. Next step was to ask a 3D printing company to create real-world models. I can know handle my creations, and look at them from any angles in a second. Here is a selection of those tries.

Doyle Spirals are a particular case of circle packing: each circle is surrounded with 6 tangent circles. When the parameters are well chosen (and this is the hard stuff), this circle packing can tile the plane. Applying to this tiling geometric transformations preserving the tangency property, one can create elegant patterns. This work was initiated while looking at the beautiful and challenging images created by Jos Leys.

The E8 Polytope is an 8-dimensional object considered by mathematicians to be the most elegantly symmetrical and aesthetically pleasing geometric object known.  Here we see 3D and 2D projections (shadows) of the 8D object.  Of particular interest are the various symmetry axes, some of which display icosahedral, hexahedral and octahedral symmetries.  The vertical symmetry axis resolves into the familiar concentric circles graph, with an unobstructed tunnel running through the complex object.

This is a test of a color map using Cinderella software.  I am interested in creating multi-color wave patterns.

I intend to use these color patterns  to wrap complex 3D forms.

As a constructional engineer, born in 1944, I am self-taught in mathematics and art.