Yes - as you "zoom in" on the sides of the snowflake, the same pattern occurs infinitely.
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For a fixed area, the perimeter is minimum for a circle, but has no maximum. Fractal figures (such as Koch snowflake) may have a finite area within an infinite perimeter.
Probably fractal geometry.
A fractal is a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole (self similar). The term "fractal" was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured." A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.
koch curve
yes! the best example would be the Koch snowflake.