Brainfilling Curves
@fractalcurves.bsky.social
Jeffrey Ventrella: fractal curve artist. fractalcurves.com ventrella.com
For my book, I'm exploring all kinds of space-filling curves, including approximations using physical simulation of particles and springs. Animations coming soon. This demonstrates very high Kolmogorov complexity compared to algorithmic recursive techniques. #fractals
Robert's polyforms provide a nice way to appreciate fractal tiling. They relate to space-filling curves in an interesting way that I'm currently exploring.
@robertfathauer.bsky.social · last wk.I added several new self-replicating tiles to my "Fractal Reptiles Based on Polyforms" website. I'll be talking about these at the Bridges Conference in Galway, Ireland this week. mathartfun.com/fractaldiver...
My upcoming book on the art of space-filling curves will cover the subject of edge-replacement vs node-replacement: two complimentary ways to construct fractal curves. #fractal #math #spacefilling #hilbert #gosper
I created a color-gradient Hilbert curve to study the nature of its sweep.
For my new book, I'll be covering Doug McKenna's more recent fractal curves. These illustrations from my previous book will be revised. I want to build some dialog here as I develop the book, so I'm not operating in a vacuum. Please vote! What would you like me to post here? My default: art!
This image shows a discovery of mine: how plane-filling curves of the same family tessellate with each other. I plan to get to the bottom of this and describe it in my new book, "Brainfillers: the Art and Math of Space-filling Fractal Curves". It will be published next year by A.K Peters/CRC Press!
Another watershed-style treatment of a plane-filling curve
James Gyre gave me this. It's based on a fractal curve he saw on my web site. I met James at Bridges Math/Art 2024. He was showing his cool wooden geometry stuff: pittsburgh.makerfaire.com/maker/entry/...
This is called "Gosper Watershed". I'm working on another watershed - it's part of a slow learning process to understand the dual relationship between space-filling curves and space-filling trees.
spacefillingcurves.wordpress.com/2016/09/27/i...
Is there a 3D Gosper curve?
The Gosper curve is one of the most amazing and satisfying plane-filling curves. The Gosper curve is a self-avoiding, plane-filling fractal curve containing 7^n segments (where n is the order of th…
spacefillingcurves.wordpress.com
This is a composite of several superimposed iterations of a space-filling curve I discovered many years ago. It belongs to the order-7 family. The corners have been rounded to make it trivially-self-avoiding. #space-filling #curve #fractal #math
#space-filling #curve #fractal #math Brainfiller Gem: The complex plane is an art canvas made of two-dimensional numbers. The integer subset of the complex plane is rich with number-theoretical potential. The Gaussian integers (square lattice) and the Eisenstein integers (triangular lattice)...
