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# Chaos Game

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Posted 23 July 2013 - 12:51 AM

Here is the effect of applying the 'game rules' to the pentagon in the shape of a home plate.  See that the empty space pattern in the pattern of the starting figure occurs again.

Also notice that this shape is irregular and not triangular.

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### #12 Rainman

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Posted 23 July 2013 - 12:56 AM

And that's why you should never go by intuition in mathematics (or at least have better intuition than I do)

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Posted 23 July 2013 - 01:27 AM

octogons anyone?

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### #14 bonanova

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Posted 23 July 2013 - 11:18 AM

But I'm not clear what happens if your initial point were inside.

Look backwards.  If the second point were in the middle empty area, where does that put the first point?

Maybe this logic can be extended to the other smaller empty areas as well...

I can't look backwards from the initial point.
If the initial point were in the central area, the second point would not also be there.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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Posted 23 July 2013 - 03:26 PM

But I'm not clear what happens if your initial point were inside.

Look backwards.  If the second point were in the middle empty area, where does that put the first point?

Maybe this logic can be extended to the other smaller empty areas as well...

I can't look backwards from the initial point.
If the initial point were in the central area, the second point would not also be there.

I asked you to look backwards from the second point.  if the second point is in the center, then there could not have been an initial point as any where twice the distance from the center is outside of the shape, therefore we could not under the rules and point system have points in the center.

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Posted 23 July 2013 - 03:27 PM

So the only point that could ever end up in the center of the shape is the initial point but the resulting image would be the same as no other dot could go in that empty space.

Edited by BMAD, 23 July 2013 - 03:27 PM.

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### #17 Pickett

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Posted 23 July 2013 - 07:27 PM

Spoiler for So maybe I have something wrong...

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### #18 Pickett

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Posted 23 July 2013 - 07:33 PM

Spoiler for trapezoid

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### #19 Pickett

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Posted 23 July 2013 - 07:51 PM

Spoiler for And lastly a stretched triangle...

Alright, I'm done now...this was just fun to do!

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Posted 23 July 2013 - 07:57 PM

Spoiler for So maybe I have something wrong...

Great point. My program allows me to tweak the ratio (or pull) to make the 'hard to see' patterns in the above drawings easier to see. I assure you the image is there yours just has more noise. But if you examined frequency by location (or clustering) the images wouuld clean up like mine. But you are right, the empty spaces in my plate examples aren't completely empty.

Edited by BMAD, 23 July 2013 - 07:59 PM.

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