Pastimes in the Euclidean

I rediscovered a childhood toy, the Spirograph:

It’s nice having more patience for it. Like all meditative piece-work, it increases focus, decreases stress.

It's on a border between drawing and copying, handwork and machine motion, intention and accident. In that sense it’s easy to pick up, one breezes through the apprenticeship…

The basic kit comes with red and blue pens, but adding color explodes the possibilities. Test patterns backlit in a window:

On tracing paper, layering is intriguing:

I’m reminded of some of the lifeforms in Ernst Haekel’s Kunstformen der Natur, or Art Forms in Nature. Here, for example, are selections of his drawings of siphonophorae, which is an order of sea creatures that float in fascinating colonies of individuals. The order siphonophorae includes the Portuguese man-o-war, which mimics jellyfish.

Some geometric constraint related to the spirals seems to be at work in these body shapes. Perhaps it has something to do with the concept of “action minimization,” the tendency of all motion to follow, basically, the path of least resistance. (I picked up this concept from The Quantum Rules by Kunal K. Das, a simple layperson’s book on quantum physics.)

These particular lifeforms have 8 repeating features of various shapes. For these colonies, does the number 8 provide some necessary biological function, within its own unique constraints of 'eightness,' via action minimization?

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The hardware for spirographic drawings, meanwhile, are more like like gears tooled to reproduce a path of least resistance for a given mathematical relationship. They sort of unveil an answer to an unknown question. With more than seven variable pen-positions on each wheel or oval or other gear shape, the element of surprise doesn’t tend to fade very quickly from the overall project.

All of this got me thinking about an absurd idea of gear drawings. What if there were huge collections of gears not 'limited' to spirals, but could be used to make actual drawings—for example realistic horses, buildings, or landscapes? Perhaps the gear sets would arrive in little suitcases, along with thick catalogs of various instructions.
 
For example: To make the horse’s neck, turn gear 42 along arc 5 for three notches. Now turn gear 22 along arc 12 for 8 notches… 

It would be the player piano of drawing. But more flexible, in that the drawings could be changed into collages of scale and proportion, expressive of the permutations of the gears. One could easily whip up some centaurs combining horses and bats…produce a fruit tree with the sequence intended for veins…style a rectangular chamber that weeps until it’s oval…