Tool

n-flake playground

For each n ≥ 3 the n-flake is a central regular polygon with n smaller copies at its vertices. Tune n to see pentaflake, hexaflake, and the polygonal family.

Number of vertices n: 5 (pentagon)

Points: 120,000

IFS rule

n = 5  (regular 5-gon)
contraction ratio  r = 1 / (1 + 2 cos(π/n)) = 0.381966

IFS: 6 affine maps, all with scale r, each with probability 1/6
  f_0:  central copy at the polygon's centre
  f_k:  copy at vertex k (k = 1..5), located at
          (0.5 + (0.5 − r/2) cos(2πk/5 − π/2),
           0.5 + (0.5 − r/2) sin(2πk/5 − π/2))

Hausdorff dim  =  log(6) / log(1/r)  =  1.8617

n = 5 is the pentaflake; n = 6 is the hexaflake.

Background at /fractals/pentaflake.

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