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This video shows six different methods of creating the Sierpiński triangle including removing triangles, the chaos game, Pascal’s triangle mod 2, the bitwise dominance order, a ternary branching tree, and the arrowhead construction.
Six Sierpiński Triangle Constructions (visual mathematics)
#chaos #ChaosGame #ChaosTheory #dynamicalSystems #fractal #fractals #GenerativeArt #Geometry #Math #MathArt #MathematicalVisualProofs #Mathematics #nowWatching #Pascal #PascalTriangle #selfSimilar #sierpinski #SierpinskiTriangle #ternaryTrees #YouTube
now for some less systematic exploration of cool ones i found. here's some with 6 points and quadratic constraints.
here's the two flakey ones.
now with two linear constraints. 2 with straight lines, 2 crinkly and 2 flakey.
but it all gets prettier when you go to 5 points or higher 😃. though they are also just more colorful thanks to the coloring scheme 😇.
(i'm leaving out all the mirror images from now on…)
next up, "quadradic" contraints. these constrain changes of velocity. the simplest being "don't move in the same direction you last moved in".
i have played around quite a bit with constraints now 🖇️.
the basic idea is to limit which target points on the basis of which target points were chosen previously. i found the sweet spot is when there are about 3 or 4 target points (= degrees pf freedom), less will give you something like Cantor dust, more tends to get noisy.
i call the easiest interesting constraints "linear": they remove options based on relative position to the previously chosen point.
okay, the color wheel is implemented, and it turns out, if you just make it one rotation the colors will just form a gradient. not un-pretty but not insightful about the structure either.
two rotations seems to work pretty great, though. :)