aurusallos: visualizingmath: The Menger Sponge is a self similar, three dimensional fractal. The con
aurusallos:visualizingmath:The Menger Sponge is a self similar, three dimensional fractal.The construction of a Menger sponge can be described as follows:Begin with a cube.Divide every face of the cube into 9 squares, like a Rubik’s Cube. This will sub-divide the cube into 27 smaller cubes.Remove the smaller cube in the middle of each face, and remove the smaller cube in the very center of the larger cube, leaving 20 smaller cubes. This is a level-1 Menger sponge (resembling a Void Cube). n=1.Repeat steps 2 and 3 for each of the remaining smaller cubes, and continue to iterate ad infinitum. Source.As the number of iterations goes up, the surface area of the “sponge” increases, but its volume decreases. This means that as n approaches infinity, the fractal’s volume will approach zero, but have infinite surface area.Image source.I love fractals. -- source link
#cool math