Growing Points IV

by Simon Whitechapel

The images below are formed by finding the points a/b of the distance between all possible pairs of n vertices of a polygon (when a/b ≠ 1/2, there are two such points, calculated first from x₁,y₁ of the pair, then from x₂,y₂). The new points are then added to the original set and the process repeated.

vertices = 5; a/b = 1/3; repetitions = 0..2

v = 3; a/b = 1/5; r = 0..3

v = 3..10; a/b = 1/4; r = 2

v = 3..10; a/b = 1/5; r = 2

v = 3..10; a/b = 1/6; r = 2

A central point can be added to the polygon, as here:

v = 3 + center; a/b = 1/5; r = 0..3

v = 4 + c; a/b = 1/5; r = 0..2

v = 5 + c; a/b = 1/5; r = 0..2

When a/b > 1, the shape expands beyond the boundaries of the original polygon, as here:

v = 3..10; a/b = 4/3; r = 2

v = 3..10 + c; a/b = 4/3; r = 2

One can also insert points between the vertices:

v = 5 + 1 x inserted; a/b = 1/5; r = 0..2

v = 3 + 1i + c; a/b = 1/2..8; r = 2

v = 3 + 2i; a/b = 4/3; r = 0..2

© 2007 Simon Whitechapel

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