antisnowflake

A fractal derived from the Koch snowflake. The base curve and motif for the fractal are illustrated below. The area enclosed by pieces of the curve after the nth iteration is A_n = A_(n - 1) + 1/3 ℓ_(n - 1)/a Δ/3^n, where Δ is the area of the original equilateral triangle, so from the derivation for the Koch snowflake, the total area enclosed is A congruent lim_(n->∞) A_n = (1 + 3/5) Δ = 8/5 Δ.

exterior snowflake | Gosper island | Koch snowflake | pentaflake | Sierpiński curve