Christian Wolf is a self-taught person who started his career as a freelance IT expert at the age of 18, envisioning early the vast opportunities of the personal computing business while completing German high school.
Working mostly as a freelance consultant under the label BHI-Systemberatung, he exposed his 25+ years of consulting and SW development experience on a wide variety of computer types and operating systems, mostly in SW projects for the telecommunications enterprise.
Considering himself a self-empowered “Apple Evangelist” way before this became a real job position, he acquired a deep knowledge on how to become productive using Apple technology.
He recently founded the “forty-two times ten GmbH“, specializing on the rapidly growing market to integrate Apple Mac OS X and iOS devices like iPad and iPhone in the business networks of midsized companies and the enterprise.
One of his more time-consuming hobbies is exploring something named “iSpace,” an actually very simple 10D integer space-time with changed distance definitions. Using Mathematica from the very beginning, he believes to have found a simple way to calculate many constants of nature from integer geometric first principles, small prime numbers, and the golden section.
Project: Mapping NKS Cellular Automata onto the Spiral Honeycomb Mosaic (SHM)
The so-called “Spiral Honeycomb Mosaic,” or SHM, is an intrinsically discrete closed space with properties similar to the Ulam Spiral, whose boundary is formed by a fractal known as “Gosper Island.” Although being a geometry with very interesting and unusual properties, it is believed to be not widely known in the scientific community outside its initial fields of machine vision, recreational geometry, and, more recently, fractal image compression.
Paul Burke wrote a Mac OS application for interactive exploration of the SHM space in 1997, the user interface of which shows a striking similarity to today’s powerful Manipulate command of Mathematica 8. He created the really nice pictures below using a so-called “Superduck” to illustrate the unusual SHM properties, whereas the prime distribution and the coordinate layout shown below have been created by myself (at that time using a C-based software module):
The output of different suitable cellular automata like Rule 30, Rule 60, and Rule 110 will be mapped onto the SHM space, conducting a systematic search for unexpected patterns or possibly interesting regularities like those of the prime distribution within the Ulam Spiral. An important ingredient to the experiment is to repeatedly apply the unusual properties of the SHM multiplication to the mapped CA images, usually using the natural SHM factor 7 until the originally mapped CA image will return after 7 steps. Using different n, it can take a very long time before it will return to the original image after multiples of the SHM space size (7^n steps), but it will always return as the HSM multiplication is a bijective operation.
An interesting outcome would, for example, be that a pattern generated from Rule 30 would show unexpected modifications to its perceived level of randomness, or that simpler repetitive patterns like Rule 60 might be transformed to suddenly show some degree of randomness. Another possibility is that certain CA patterns might just show an increase or decrease of their perceived complexity, and it should be helpful to optionally highlight the position of prime numbers in the SHM space.
If the mapping reveals some interesting properties, the notebook will be converted into a suitable form to be placed in the Wolfram Demonstrations Project. And, of course, it will show the “Superduck” image of Paul Burke, because I really, really like it.
Favorite Four-Color, Four State Turing Machine