https://en.m.wikipedia.org/wiki/Moiré_pattern
This is found in magic angle graphene, which will likely yield a Nobel Prize in a few years: https://www.quantamagazine.org/when-magic-is-seen-in-twisted...
I wonder if there is a connection to these spirals and their segmentation lengths…
ps: how funny, your description reminded me of a nightmarish manga about a strange hole in a mountain, and .. it was by junji ito https://www.scaryforkids.com/enigma-of-amigara-fault/ (I forgot who the author was until right now)
I'm surprised by that definition and always thought of a spiral as a curve with a monotonic signed-curvature function.
So, for example, the Euler/Cornu Spiral has a point of inflection where the curvature changes sign at the point of inflection, but the curvature increases continuously all the way from -infinity to + infinity as you travel along the length of the curve. So under my definition the whole Euler Spiral would count as a spiral, even though it stops revolving/emanating from a point just under 1/4 turn after the inflection point.
If you split a curve into segments at its curvature minimum and maximum points (vertices in the differential geometry sense [0]) then each segment has monotonic curvature and I'd define those as spiral segments. Vertices and monotonic curvature segments are preserved under inversion, which is mathematically useful.
In contrast, inflection points with zero curvature are not preserved under inversion. So the Euler spiral can be transformed by a suitable inversion to a curve like the one defined by Wikipedia, that is a curve emanating out from, for example, the origin.
Edit: just spotted this in the Wikipedia article on spirals 1]:
> Spirals which do not fit into this scheme of the first 5 examples:
> A Cornu spiral has two asymptotic points.
> The spiral of Theodorus is a polygon.
> The Fibonacci Spiral consists of a sequence of circle arcs.
> The involute of a circle looks like an Archimedean, but is not:
The Cornu spiral I've covered.
The spiral of Theodorus doesn't have a monotonic curvature function - it's a polygon approximation of the Archimedes Spiral, which does.
The Fibonacci Spiral's curvature function is a monotonic step-function.
The involute of a circle is a log-aesthetic curve, all of which have monotonic curvature functions. (The logarithmic spiral and the Euler spiral are also log-aesthetic curves.)
Let's say the spiral has rotated 6000 degrees, and I'm approximating it with 100 points (one point every 60 degrees) and line segments. Well, a hexagon is nothing other than 6 points chosen 60 degrees apart from each other at the same distance from a central point, connected with straight lines. The same thing holds for a square at, e.g. 9000 degrees.
Check out these images to see what I mean: https://imgur.com/a/mvIVuch
https://www.youtube.com/watch?v=PpyKSRo8Iec
https://www.youtube.com/watch?v=kw9wF-GNjqs
They can form very neat patterns.
Anyone who knows how to implement this with projectM, or GLSL?
