def sierpinski(x, y, size): half = size / 2 return ( sierpinski(x, y, half), sierpinski(x + half, y, half), sierpinski(x + half / 2, y + half, half) )
fractal = sierpinski(0.0, 0.0, 1.0)The Scale
What happens when the scale varies but the pattern remains the same?
Development of Move 1
It's interesting that fractals encompass so many different fields that I could have selected most of the available forms. And in each of those fields, though theoretically possible, they run into practical constraints just like in the code snippet where you might end up with an error due to infinite recursion.
Development of Move 2 — Yet our imagination can execute the code with no terminating condition, showing no signs of fatigue.
The infinite is nowhere to be found in reality, no matter what experiences, observations, and knowledge are appealed to. Can thought about things be so much different from things?
David Hilbert, On the Infinite (Über das Unendliche), tr. Erna Putnam and Gerald J. MasseyDevelopment of Move 3
I like the quote and it's true that infinity really does lie only in how we think about things. I was trying to see if there are any counterexamples such as time after a person's death or the scale of the universe. Part of the problem is the lack of our ability to measure the infinite - what is observable is by definition finite.
Contrast of Move 4 — Connecting to the concept of infinite scale invariance, a Shepard tone treats frequency as the shifting scale and pitch class as the repeating pattern. Yet, this endless fall is merely a trick of perception, succeeding only because it masks itself within the hard physical boundaries of our biology.
Pitch_Paradox_down.mp3
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