List of fractals by Hausdorff dimension

According to Benoit Mandelbrot, "A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension.

"[1] Presented here is a list of fractals, ordered by increasing Hausdorff dimension, to illustrate what it means for a fractal to have a low or a high dimension.

(golden ratio).

(golden ratio).

Images generated with Fractal Generator for ImageJ.

(golden ratio).

(golden ratio).

(golden ratio).

Using the central triangle as the base, form a tetrahedron.

Replace the triangular base with the tetrahedral "tent".

Note that there are marked differences between Ireland's ragged west coast (fractal dimension of about 1.26) and the much smoother east coast (fractal dimension 1.10)[40]

The quadric cross is made by scaling the 3-segment generator unit by 5 1/2 then adding 3 full scaled units, one to each original segment, plus a third of a scaled unit (blue) to increase the length of the pedestal of the starting 3-segment unit (purple).
Generator for 32 segment 1/8 scale quadric fractal.
Generator for 50 Segment Fractal.