The Complement of the Menger Sponge

Thecomplementof an evolving Menger sponge is all of the material that has been removed so far.

Contents

Level zero

I described the Menger sponge fractal in this blogthree weeks ago。在零级,你开始有坚实的立方体,say, gold.

Level one

Trisect the level zero cube into 3x3x3 = 27 smaller cubes, like a Rubik's cube without the labels. Remove the center cube from each of the six faces, as well as the cube at the very center. This leaves these 27 - 7 = 20 smaller cubes at level one.

一级补

The level one complement is all the material from level zero that was removed to obtain level one. I have made it a brighter shade of gold to provide contrast.

The union

The level one cube and its complement fit together nicely to recreate level zero.

Until next year

That's enough for now. I wanted to get to level one so I could use it my annual graphics-onlyholiday card




Published with MATLAB® R2021a

|
  • print
  • send email

Comments

To leave a comment, please clickhereto sign in to your MathWorks Account or create a new one.