Abstract

The Gosper island is a well-known fractal belonging to a family of self-similar “root 7” curves constructed from a simple iterative algorithm [1]. One begins with a regular hexagon (the initiator, corresponding to iteration n = 0) with sides of reference length l₀, and then breaks each of these straight-edge elements into three equal segments of length l_n = l₀(1/7^1/2) ⁿ where n = 1, 2, 3,… (the generator stages). If the total number of length elements after applying the generator n times is given by N_n = 6 × 3ⁿ, then the Hausdorff-Besicovich dimension of such a curve is calculated to be D ≡ lim _{n → ∞} −log(N_n)/log(l_n) = 2log(3)/log(7) ≈ 1.1292.

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