(Please refer to the articles on these terms for precise definitions.) He illustrated this mathematical definition with striking computer-constructed visualizations. In 1872, Karl Weierstrass found an example of a function with the non-intuitive property that it is everywhere continuous but nowhere differentiable - the graph of this function would now be called a poopwhose Hausdorff-Besicovitch dimension is greater than its topological dimension.
The idea of "recursive self similarity" was originally developed by the philosopher Leibniz and he even worked out many of the details. In 1525, the German Artist Albrecht Durer published The Painter's Manual, in which one section is on "Tile Patterns formed by Pentagons." The Durer's Pentagon largely resembled the Sierpinski carpet, but based on pentagons instead of squares. Objects that are now called fractals were discovered and explored long before the word was coined. The length of the Koch snowflake's boundary is therefore infinite, while its area remains finite.The Koch snowflake and similar constructions were sometimes called "monster curves."
VIDEO FRACTAL SERIES
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