# Graphic Layers, Splitting Regions, Symmetry Operations to Font Characters

As Stephen Wolfram wrote in his lates blog post:

A basic interactive system for generating logos is a tiny amount of Mathematica code. But getting everything exactly right turns out to be quite tricky, and to involve some quite sophisticated mathematics. It’s easy to apply symmetry operations to regions representing font characters. The issue is rendering them. The most obvious thing is to layer them in the order they’re generated. But if the regions overlap, then doing that can break symmetry. And the only way to guarantee to preserve symmetry is to do some intricate computational geometry, breaking up the regions just right.

1. Does someone have an idea what he meant? Most of you probably know the MomathExplorer from Chris Carlson. Why did that normally work out on a desktop system, but not on a desktop system in Momath museum?
2. How to generate layers anyway in Mathematica for graphical objects?
3. How to prevent regions that overlap, to break symmetry?
4. How to break up regions just right?

I can't really imagine what was going wrong and to be honest this sounds a little bit confusing.

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I guess your "Does someone have an idea what he is meaning? " is going to cost us an heptagonal legal problem –  belisarius Dec 19 '12 at 20:06
What do you mean? 18, 35, 112 problems? Was it wrong to ask what he actually meant? Because I don't get it... –  Stefan Dec 19 '12 at 20:12
In the CDF, try changing the radial distance so that it overlaps. Now stop and follow the pattern of overlap between adjacent symbols (e.g., leg of the first λ under the stem of the second λ, leg of second λ under the stem of the third and so on). At some point, this pattern will break (or you can make it break by changing the rotation/distance, etc). This is what he means by breaking the symmetry, which is not a nice thing to have in a logo (esp. a math logo that's supposed to be derived from symmetry operations). As for belisarius' comment, just ignore him; it's more of an inside joke now ;) –  rm -rf Dec 19 '12 at 20:12
I see. Wow. Obviously I'm to impatient to find something like that...ok...that's #1. Thank you –  Stefan Dec 19 '12 at 20:17
Presumably you've seen "Both a Logo and an Exhibit: Mathematica and the Museum of Mathematics Logo Concept" : youtube.com/watch?v=CCTa904eRfM –  cormullion Dec 19 '12 at 21:40