Euler's Cistercian Logarithmic Spiral (First 4800 decimal digits)
I did this one early, as I'm going to be busy tomorrow. I found a reference for digits of Euler's constant, 2.71828459045... that's as far as I know, which is more than I ever really need to know, of course. As e is an irrational number, I claim that it goes on forever without repeating. Like pi, or a bunch of those other irrational numbers. Phi. Square root of two.
To make things more interesting, I implemented a Cistercian number glyph renderer based on what I read here: https://en.wikipedia.org/wiki/Cistercian_numerals - the Cistercian monks in the thirteenth century had a way of encoding 4 digit numbers (0 to 9999, though I'm not sure if they actually used 0). I took quads of digits from my stream of decimal digits of e and turned them into Cistercian numerals - the first glyph can be decoded as being 2718, and then the next glyph is 2845, and then 9045. After that, I gave up checking.
100 digits around the spiral, and we've got back to the top again, but at a smaller radius, and drawing our numerals just a little smaller. I did some math, where I knew I wanted each full loop to become a certain fraction smaller (around 5%, I forget what the final value was), so each loop of 100 digits, I'd have scaled by a factor of 0.95 - so the incremental scale factor from one digit to the next was 0.95 ^ (0.01). All that exponential math makes me feel like Euler might have been proud.
There are 12 loops here of 100 Cistercian digits each, so that's 4800 decimal digits of e. If you look long enough, you'll find any series of digits (your ZIP code, your PIN, your SSN) in irrational numbers like this. Because the Cistercian digits hold 1000x more information per digit compared to our decimal digits, it's going to take you 1000 times longer to find a series of digits of a given length.
The digits don't repeat, and they don't even come around very often.
Tools Used: DrawSVG, e
Languages Used: Python3
Development Time: ~1.5 hours
Drawing Time: ~45 minutes
What's Generative Here: The glyphs here represent the digits of e, which gives me an unending series of data.
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