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Fractals I created over Christmas Break

I spent some time over Christmas Break making some fractals with my fractal program. The first thing I did was figure out an easy way to make space filling curves. Space filling curves are usually done by l-system fractal generators (whereas mine is an IFS fractal generator) but the "connect lines" function in my program allows me to create them as well. I made quite a few space filling curves, some invented myself, some inspired by designs I saw on this website. The one that forms the Koch Snowflake (the fourth one) is already well known, but I recreated it just because.

The second thing I started messing around with is a motif that forms half of an isosceles triangle. First thing I discovered was two space filling curves I hadn't seen before. These surprisingly filled the spaces with a self-avoiding pattern without any need for me to use the "connect lines" function of my program.

The second thing I discovered were several motifs that formed very interesting fractal patterns. Two of these were very rectilinear, which is very odd considering the fact that the motif itself is formed out of a 60 degree triangle. The filled in white areas in the following images are entirely filled in by the path that the curve takes; however the curve is not always self avoiding so I was not able to make them all into space filling curves.

I hope you enjoyed my little gallery.

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