Trirographs

Toby's recent formula upload to the Ultra Fractal Formula Database, spiroglyphics, reminded me of a formula I wrote several years ago. It's a Trirograph. A trirograph is a spirograph with three wheels, rather than two. One wheel is fixed, and the other two rotate. It's rather hard to visualize how it would work mechanically, like the traditional spirograph that many of us played with as kids. But, mathematically, it works rather nicely. I need to get the formula cleaned up and make it available publicly. But, that's just one more in a long list of projects that I'll get to eventually.

I found the Trirograph several years ago while doing web searches when I was working on a spirograph formula.

Images can be simple, looking like they may be a traditional spirograph.
Images can be more complex.
Images can be a jumbled mess.
Images can be plotted by using points, rather than lines, if desired.
Multiple iterations of the same shape can be drawn with changing some of the parameters for each iteration allowing for a variety of overlapping effects.
Or, if one prefers, shapes rather than lines or points can be used.
Or, use spirals to connect the points along the path.
None of these examples are intended to be great art. I just consider them fun. In the right hands, even the simple spirograph, or trirograph in this case, can be turned into attractive art work. At least, I think so.