An Optical Demonstration of Fractal Geometry

Clockwise from top left: Sierpinski Triangle, image of the stacked sphere configuration,
image of the Sinai cube, ray tracing of the Sinai cube, ray tracing of the stacked spheres, scaling plots of
the box counting analysis of the Sierpinski triangle (lower dashed blue) the stacked spheres (lower solid
black), and the Sinai cube image (upper dashed red) and ray tracing (upper solid green)

Billy Scannel, Ben Van Dusen, Richard Taylor

We have built a Sinai cube to illustrate and investigate the scaling properties that result by iterating chaotic trajectories into a well ordered system.

We allow red, green and blue light to reflect off a mirrored sphere, which is contained in an otherwise, closed mirrored cube. The resulting images are modeled by ray tracing procedures and both sets of images undergo fractal analysis.

We offer this as a novel demonstration of fractal geometry, utilizing the aesthetic appeal of these images to motivate an intuitive understanding of the resulting scaling plots and associated fractal dimensions.
Read more: http://arxiv.org/ftp/arxiv/papers/1209/1209.2182.pdf

Fractal Dimensions Should Modify The Casimir Effect

The effects of fractal dimensions could one day be observed if Casimir measurements can be made sensitive enough, according to theoretical physicist
Back in the 1920s, Theodor Kaluza and Oskar Klein developed an idea that unified Maxwell’s theory of electromagnetism with Einstein’s theory of relativity.
That was an impressive feat but it had one small drawback. In the Kaluza-Klein model, the universe has 5 dimensions.
Kaluza and Klein were unfazed, however. They suggested …. Continue reading Fractal Dimensions Should Modify The Casimir Effect