Star Fractals

by Simon Whitechapel

Star fractals are created by finding the v₁ vertices, lying at distance r₁, of a star whose center is (x₁, y₁). Each vertex is then to form the centre, (x₂, y₂), of a star with v₂ vertices lying at distance r₂ = r₁ x rm; and so on. The process is illustrated here (in the final stage of the animated gif the stars are not given arms, only vertices):

vertices = (4, 6, 5, 3, 5); rm = 0.5

Left: v = (4, (2..10), 4, 4, 4)
Right: v = (4, 4, (2..10), 4, 4)

v = (3, 3, 4, 6, 4)

v = (6, 3, 5, 4, 4)

v = (5, 6, 3, 5, 4)

v = (4, 5, 6, 4, 4)

v = (4, 6, 5, 5, 3)

v = (6, 3, 5, 4, 3)

v = (6, 6, 4, 6, 5)

v = (3, 4, 3, 5, 3)

v = (6, 4, 5, 3, 3)

v = (4, (2..7), 3, 6, 5)

v = (3, 4, 10, 4, 4)

Here the variable rm changes while v remains the same:

v = (6, 4, 5, 5, 4); rm = (0.35..0.65); rmi = +0.05

© 2007 Simon Whitechapel