Growing Points V

by Simon Whitechapel

To create these images, begin with the vertices of a v-sided polygon, 1..v, and pair each with the center of the polygon, x_c, y_c, to create a set of pairs having the form (x_1..v, y_1..v; x_c, y_c). For each pair, find the point that is a/b of the distance, d, from (x_1..v, y_1..v) to (x_c, y_c). Using this point, generate two more points lying at (θ + θ₁) x d x dm and (θ + θ₁ + θ₂) x d x dm, where θ is the angle between the original pair and θ₁, θ₂ and dm are variables. Replace the old set of pairs with these new pairs and repeat:

v = 4; a/b = 1/2; θ₁ = 0.785 radians; θ₂ = 2.847 rad; dm = 0.5

Here are more completed examples:

v = 4; a/b = 1/2; θ₁ = 0.785; θ₂ = 3.288; dm = 0.5

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v = 4; a/b = 1/2; θ₁ = thi=0.785; θ₂ = 3.583; dm = 0.5

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v = 4; a/b = 1/2; θ₁ = 0.703; θ₂ = 3.437; dm = 0.5

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v = 4; a/b = 1/2; θ₁ = 2.848; θ₂ = 3.671; dm = 0.5

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v = 6; a/b = 1/2; θ₁ = 0.186; θ₂ = 3.435; dm = 0.5