APOD: Quantum Steampunk Fantasy Fractal... (2013 Dec 30)

[Douglas]

Any work done on modeling Van Derwaals forces with fractals?

[DavidLeodis]

The mention of fractals reminds me of the fun rhyme:-

Bigger fleas have littler fleas upon their backs to bite em.
And littler fleas have littler fleas and so on ad infinitum.

PS. As mentioned by an earlier person should not the APOD title use "Steampunk" (as used in the discussion of the APOD and the APOD archive list) and not "Streampunk".

[neufer]

As I recall, the dimensionality of the ordinary Mandelbrot set is between 2 and 3, so shouldn't the dimensionality of this fractal be greater than 3, rather than 3?

Presumably the boundary surface of the Quantum Steampunk has a Hausdorff dimension of 3.

The Hausdorff dimension of the boundary of the Mandelbrot set equals 2 as determined by a result of Mitsuhiro Shishikura. It is not known whether the boundary of the Mandelbrot set has positive planar Lebesgue measure.