Kaleidoscope My kaleidoscope images were created in Mathematica. For a point (x, y) in the triangle,See an example of a parent and its seven offspring.(x, y) -> (y, x) is a reflection across the line y=x The process is repeated N times. Each time, a new parent triangle is chosen at random with a new color and its seven offspring are created. By increasing the value of N the design changes. See Image 2 I adjusted the procedure so that the parent triangle was a right triangle. See Image3 I got tired of triangles and used circles to create the next group of images. A parent circle is chosen with a fixed radius and random center. The seven offspring are created with the same reflections as above. See an example of a kaleidoscope image with circles. Finally I let the radius vary along with the center. Here's an example. I ran the program again using line segments. Image 8 shows the result. eobrien@gmu.edu |