Wednesday, January 28, 2009

Four Color Map Theorem

I hope Mr. Toby doesn't mind but this post has nothing to do with him (although, being a star himself, he will probably not mind yet another star story).

Per usual, click the pic.

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6 comments:

Tobee 'n DeeDee said...

Beeooteefull! I can see another constellation forming, but I am not sure what it is yet.

January 28, 2009 at 4:21 PM
Tobee 'n DeeDee said...

Tobee welcomes awl blog posts, whether dey r aboot him or nutt. Da mowa posts da betah!

January 28, 2009 at 4:53 PM
Chip Bradley said...

Incredible star. I completely love it. I can see I need to brush up (no pun intended) awn my n-point stah tekneeks. These are amazing.

January 30, 2009 at 4:52 AM
Chip Bradley said...

I'm curious about something. Briefly, can you explain how you found the right "way" to paint this star? If this is not a brief answer, you can provide a separate link -- which I am sure would also prove to be interesting. Thanks.
If I had to paint this star, I think I would have winged it by using pennies, nickles, dimes and quarters to represent the colors. Would that "work" for you, or is there a better "Lee" way?

January 30, 2009 at 5:18 AM
Tinyc Tim said...

I like your "nickel and dime" approach. I use a pencil (which has a good eraser) and pick an arbitrary piece and give it a color. Then I move to an adjoining piece, look at all its neighbors and pick a color that does not violate the condition. I continue in this way till I hit a snag, back up, try a different color and then move forward again. Eventually, I get all the pieces assigned.

(I then paint it and discover I screwed up and ...)

I expect this could be computerized. You'd have to represent the puzzle in some useful way. Number each piece and record, for each piece, all the piece numbers that are linked to it (i.e. touching along an edge). Then, somehow, write a routine that does what I just wrote above.

fourcolor.tc anyone?

PS - Don't try it. It sounds hard.

PPS - I cut a new Blue Moon. This puzzle does not of course have 4 colors but it does have 1 (plus wood) and, now, no blue piece touches any other blue piece. There's a link near the bottom of the page you'll see if you click the above link that will show you the new puzzle (and will reveal how I've discovered you can display it!)

January 30, 2009 at 9:17 AM
Tinyc Tim said...

Here are some early thoughts on how you might automate the "four coloring" of a map (or the pieces in a wooden jigsaw puzzle).

February 1, 2009 at 3:53 PM

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