# Star Polygon Orbit Trap

Star Polygon is a Fractal Science Kit fractal generator orbit trap based on a construction called a Star Polygon described in:

Eric W. Weisstein. "Star Polygon."

From MathWorld--A Wolfram Web Resource.

Options are provided to control the Center, Radius, Angle of rotation, and style used to display vertices (Corner Style).

A Star Polygon is 1 or more component polygons generated from a set of N equally spaced points around the circumference of a circle. A step size S is used to define a Star Polygon. The component polygons are generated as follows: starting with vertex 1, add the step size S to the vertex to generate the next vertex. Continue adding S to the previous vertex until the next vertex falls again on vertex 1. If each of the vertices has been visited, the generation is complete, resulting in a single polygon. Otherwise, start with vertex 2 and generate a 2nd polygon. Continue, starting with vertex 3, 4, etc., until all vertices have been visited. For example, if the base polygon is a hexagon and the step size S is 2, we will generate 2 polygons (triangles) with vertices 1, 3, 5 and 2, 4, 6, respectively.

The Star Vertices section has 2 properties: Vertex Count and Vertex Steps. Vertex Count is the number of vertices in the base polygon (N). Vertex Steps is a comma separated list of step sizes (S). For each S in Vertex Steps, we employ the above algorithm to generate a Star Polygon. The set of all such polygons is used as the resulting orbit trap. The trapped point's Index is set to a value between 0 and M-1 where M is the number of items in Vertex Steps and is the index of the Star Polygon that trapped the point.

See Trap Options for a description of the remaining options.