I received an interesting email this morning. Someone contacted me through my Fine Art America site requesting that I make a print available. I forgot to ask how she found the image, as I hadn't even posted it there yet. Anyway, it turns out this person is the daughter of Karl Menger, who's most famous popular contribution to mathematics (according to WikipediA), was the Menger sponge, a three-dimensional version of Sierpinski's carpet. The Menger3 formula (and other forms of it) certainly seem to be some of the most widely used and popular formulas for many that use Mandelbulb 3D.

The image she was interested in was one I recently posted here at DA, Wreck Of The Menger. Eve pointed me to a very interesting video that explains the Menger sponge quite well, Mathematical Impressions: The Surprising Menger Sponge Slice. I highly recommend that you take the time to check it out! She also had this to say about the video:

"The narrator mentions that this diagonal slice was not "discovered" till 2007.  That is inaccurate.  That slice was on exhibit at the Museum of Science and Industry in Chicago years earlier."

While Menger3 was not the only formula used in that image, the influence is evident. I use it quite often myself as it can often lead to incredible structures of simulated fantasy architecture. While I'm at it I wanted to take this opportunity to thank all those responsible for making my artwork possible, including, but not limited to Jesse at Fractal Forums for creating the Mandelbulb 3D software, Luca (aka dark-beam ) for creating many of the formulas and also Karl Menger and Benoit Mandelbrot for their dedicated work in mathematics which makes it all possible. Also thanks to all my watchers and those that fave my work too!!!

PS: Help support Fractal Forums. You can order a Fractal Forums calendar at the Fractal Forums shop.

Hal