the speed of light is the maximum speed of information transmission.
if you have planck time(aka 1 iteration) and planck length as smallest units and information doesn’t travel from one lenght to the next instantanious but within one planck time/iteration, this results in the maximum speed of information transmission, the speed of light.
information in the mandelbrot set is the border itself. it is a 1d-line, but it is filling the 2d-plane with information. the equivalent of 3d space and 4d time is our reality, our universe.
information is the essential property of a fractal. a line has no information, a plane has no information. perfect geometries like a circle or a cube only have compareably little information. but a fractal is infinite information, nothing but information of the balance between the dimensions of a line and a plane (or space and time)