Hilbert Curve


A Hilbert curve is a continuous fractal space-filling curve first described by the German mathematician David Hilbert in 1891.

Fractal's self-similarity

Fractal curves retain their original shape even if they are greatly enlarged. Most fractal curves produce the same transformation over and over on smaller and smaller scales.
The property of maintaining the original shape even when the scale changes are called 'self-similarity.'
Self-similarity is easily found around us.

An example of self-similarity

For most coastlines, it isn't easy to know whether the coastline is enlarged or reduced without other comparisons.
If you stand between the two mirrors installed inside the elevator, you can see my image getting smaller and smaller by infinite reflection.
A slice of broccoli cut out completely resembles the original large broccoli.