The Koch curve is a fractal curve constructed by recursively adding smaller equilateral triangles to each side of an initial equilateral triangle, resulting in an infinitely complex, self-similar shape. At each stage of construction, the curve has a finite length, but its total length becomes infinite as the number of iterations approaches infinity. The Koch curve stands out among other geometric shapes for its self-similarity and fractional dimension.

This video features animations to illustrate the step-by-step construction of the Koch curve with increasing complexity and explore its intriguing properties, underlying the mathematical beauty of fractal geometry.


This video is produced with the animation engine Manim.
Manim — Mathematical Animation Framework. [ Ссылка ]


Manim Animation
[ Ссылка ]


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