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Mobilelectro In reply to MichaelFaber [2007-10-27 22:48:14 +0000 UTC]

I left my reply at Michael's link above.

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Mobilelectro In reply to JoelFaber [2007-10-27 22:17:37 +0000 UTC]

Wolfram's escher map equation must be an approximation of the Escher grid then. One of the main characteristics of Escher's grid is that it repeats itself ever smaller in the center as well as rotationaly around the outside of the grid.

Hendrik Lenstra project created the right geometry seen at the link above and by using + and - parameters was able to create a variety of other grids that had the same properties. All of these grids have an exponential quality to them and reduce to infinity at the center.

Wolfram's map rotates around the center only. There is also no way to set the parameters to get the variety of grids that Hendrik Lenstra's team produced or even an acurate reproduction of escher's own version.

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JoelFaber In reply to Mobilelectro [2007-10-28 03:10:34 +0000 UTC]

No, Escher's Map doesn't approximate anything. It is the same transformation that Escher did in the painting. The Lenstra project has extended that transformation to do something that MC Escher never did. Escher left a blank spot where Lenstra has added recursive iterations.

I'll take a look at adding the extension in. It looks like it might be cool. It might be difficult to make it look smooth though. I'd have to figure out probabilities and areas so the density stays as even as possible in the repeated sections.

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Mobilelectro In reply to JoelFaber [2007-10-29 23:38:17 +0000 UTC]

Hey Joel,

You said---(I'd have to figure out probabilities and areas so the density stays as even as possible in the repeated sections.)

After playing with this variation for a while I think this is also a problem with the variation in it's present state. It is nearly impossible to get rid of the seam where it connects back around to itself which diminishes the unity of the image although the visible seam can also create interesting but different effects in its own way.

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JoelFaber In reply to Mobilelectro [2007-10-30 00:59:11 +0000 UTC]

There is nothing anybody can do about that. That's just the way Apophysis works.

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Mobilelectro In reply to JoelFaber [2007-10-28 05:49:00 +0000 UTC]

That sounds very cool if you can pull it off. I did finally work it out on this newer image. [link]

The scale thing was the trick ( 1 - 256) on the variables and then zooming into the image enough the see the reduction of scale in the center.

By the way, you're right, Escher's print does not reduce like you say and has his signature in the middle but the grid he made does reduce and you can read about it in Escher's The Magic Mirror book. He noticed it repeating itself smaller and smaller into the center and the grid he made almost completely fills in at the center unlike the print gallery image.

I think I understood how the Lenstra project differed from Escher's print.

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Mobilelectro In reply to StitcherLadyxx [2007-10-27 04:45:31 +0000 UTC]

Thanks, I had hopes the escher variation would produce a grid form more like the original escher grid it is based on however it can create some different kinds of distortion.

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