This image is an illustration of the recursive process of generating a Menger sponge, which is a fractal object. It shows the first three iterations of an infinite process. The illustration was created by using a simple "Lindenmayer system" (L-system).

The number of cubes at a given iteration is ${\displaystyle 20^n}$, where ${\displaystyle n}$ is the number of iterations performed on the first cube:

At the start, no iterations have been performed so ${\displaystyle 20^0=1}$. The image shows a total of 8,421 cubes (the sum of all four steps).

See also:

• en:L-system
• en:Menger sponge

Image: User:Solkoll. Public domainPublic domainfalsefalse This work has been released into the public domain by its author, Solkoll. This applies worldwide. In some countries this may not be legally possible; if so: Solkoll grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. More 3D fractals from my tool: Image:3D Cantor set.jpg Image:3D Julia-set (IFS 001).jpg Image:Dragon trees.jpg Image:Fractal tree (Plate b - 1).jpg Image:Fractal tree (Plate b - 2).jpg Image:Fractal tree (Plate b - 3).jpg Image:Fractal weeds.jpg Image:Harter-Heighways dragon curve (3D twist).jpg Image:Heavy Lévy.jpg Image:Julia set (reversed formula 3D).jpg Image:Lévy's C curve (3D-goggles).jpg Image:Lévy C curve (3D-twist).jpg Image:Menger sponge (IFS).jpg Image:Menger sponge (Level 1-4).jpg Image:Sierpinski pyramid.jpg Image:Sierpinski tetrahedron.jpg Image:Sierpinski tetrahedron (Detail).jpg All freaktal images are from self-written tools. Linear fractals from my : "3D IFS studio" and "3D DTIFS" (dragon trees), non-linear IFS from "3D RJIFS" (3D rev Julia).

See also: Solkoll & Solkoll 2D