The Koch snowflake is a classic fractal. It, like many other similar fractals, can be made a number of ways (IFS, Sierpinski hexagon, L systems, trees, more?). The usual way to make it is to draw an equilateral triangle, then for every line, draw a new equilateral triangle that has one edge along the middle third of the line. The process of replacing each line with a line that has a spike in the middle is repeated until you have the image below. I found the point of the added triangles by first finding the 2 points that separate the lines into thirds, then rotating the point that lies further counter clockwise and rotating it 60 degrees clockwise around the other point.
The modifications of the normal figure found here were made in several ways. Some where made by rotating the point counterclockwise rather than clockwise at varying times (e.g. every third triangle piece). Others were made by rotating it by different angles. One of the videos was made by varying things in a way I have not analyzed enough to understand; I believe it varied both angle and radius but if so it was done indirectly through rotation matrix shenanigans.
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| Koch |
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| Anti-Koch |
Video time!!!!
