Here is the Vicsek fractal.

There are two ways of constructing it. Starting from a (black) square, iteratively remove a checkerboard pattern rotated by 45°, scaling it by a factor 3 at each step.

Or iteratively remove a square pattern of squares of width 2/3 with voids of width 1/3, again scaled by a factor 3 at each iteration.

Instead of "removing" these patterns, imagine that a function is defined on the plane, and we are modifying its value at each iteration depending on whether the pixel is in the pattern or not. The final value of the function at each pixel then determines a shade of grey. This yields interesting dense fractal pattern, in which the Vicsek fractal is still recognizable as the set of pixels that are perfectly black. Here are the pictures obtained from the two patterns above.

Changing the scaling factor from 3 to some other integer yields other interesting dense fractal patterns.

Attempts by Dall-e at reproducing the Vicsek fractal...