#fractals #spacefilling #curves #brain Images for my book proposal. More deets coming...

#fractals #curves #math #geometry #art #design

#fractals #curves #math #geometry #art #design This is a variation of the Gosper curve I discovered and showed in BrainFillingCurves.com

#fractals #curves #math #geometry #art #design drawn with one line.

one line

#fractals #curves #math #geometry #art #design #space-filling

#fractals #curves #math #geometry #art #design #space-filling Plane-filling curves of the order 4 family, whose generators consists of segments with length 1 or square root of 2. This image will be published in a book soon - TBA.

#fractals #curves #math #geometry #art #design #space-filling This is a place-filling curve with 5-fold symmetry. Notice the many nested pentagons. Tell me what you think of this conjecture: all self-similar plane-filling curves with local 5-fold rotational symmetry are necessarily aperiodic.

#fractals #curves #math #geometry #art #design #space-filling Four plane-filling curves of the order 7 family. Gosper curve at the bottom, 7-dragon at bottom-left. The large one is "Gosper Dragon", which I discovered. They all have "Gosper skin" and so they can tessellate. fractalcurves.com

just two small changes

#fractals #curves #design #space-filling #math This space-filling curve is rendered at low iteration so the details are visible. When iterated to more fractal levels, the details become smaller. No matter how resolved, the curve is always self-avoiding. Notice the dense areas. A curious property.

#fractals #curves #math #geometry #art #design #space-filling This is "Brainfiller"- the mascot of my book "Brainfilling Curves", and one of the designs that will be explained in a new book I am starting to write about the art and math of plane-filling curves. More to come. The adventure begins!

#fractals Hello World.