I thought Mandelbrot was a German bread..Snail shells more closely resemble the Fibonacci progression.
1+1=2, 2+1=3, 3+2=5, 5+3=8, 8+5=13 and continuing to be as large as the constructure needs to be. It becomes very strong!
This progression is used in development of certain horn shaped musical instruments as well, but with predictable log fractions of each dimension, instead of whole numbers.
I can't remember if it was Mandelbrot or one of his students that proved, using fractal geomtry, that the shoreline around the main isle of Great Britain was indeed, infinitely long.