infinite coastlines
A free fractal demo — play it in your browser, no install. An interactive guide to the coastline paradox and fractal dimension: measure an island with shrinking rulers, build a Koch snowflake, and zoom into the Mandelbrot set.
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Open the live demo Source on GitHubFrom the README
How long is a coastline? It depends on the length of your ruler, and the closer you look, the longer it gets. Six interactive charts on the coastline paradox and fractal dimension, from a ruler survey of an island to the edge of the Mandelbrot set. No sign-up and no libraries.
The island starts as a lumpy 12-sided outline. Each segment's midpoint is pushed sideways by a random amount proportional to the segment's length, repeated 11 times (24,576 points). Each level doubles the pieces and scales them by r = √(1 + 4g²) / 2, so the curve is self-similar with dimension log 2 / log(1/r).
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