Hyperbolic Tiling Challenge

http://www.josleys.com/show_gallery.php?galid=325


http://en.wikipedia.org/wiki/Hyperbolic_geometry
http://www.bugman123.com/Hyperbolic/index.html

https://www.google.com/search?q=hyperbolic+tiling

part 2

part 4

see this also ->Hyperbolic Planar Tesselations

Tilings of Hyperbolic Spaces

lots of links about this topic

Otherwise for inspiration there's Artmatic 5 which does a lovely job with these kinds of things that don't exist in FilterForge. But annyway....

http://mathworld.wolfram.com/ConformalMapping.html

http://www.hypatiasoft.fr/Folder_Seam...ker_A.html

They're both drawn on complex planes. Which is why they're similar. Just the formulas for deriving at them is different. (Now I feel dumb typing that because I just stated the obvious.)

Actual hyperbolic tiling is seriously tricky to achieve, but since we gotta start from somewhere, here's my first attempt to fake something similar.

True hyperbolic tiling doesn't distort the image this much. It is more like a fractal.

At a different circular repeat:

This may be better.

It is still fractal circular tiling, not hyperbolic.

I'm obsessed with figuring this out. I'm lost though. I don't understand the "complex plane" math.

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Uberzev wrote: I'm obsessed with figuring this out. I'm lost though. I don't understand the "complex plane" math.

I don't know how to do this without scripting, and it would take days to write the script.

Even making a fake version with actual hyperbolic tiling (but without going into infinity at the edges) would be quite a challenge without any scripting.

I will be amazed if someone does it.

By the way, it seems that this would be the "easiest" hyperbolic tiling -- or at least the most useful for square images -- as each of the tiles are hyperbolic squares, thus the image would tile seamlessly.

If you can make it, that is.

I think that most probably to make this is much more complex than it seems, at least to program, and would need a complex custom software to make it probably, OR perhaps could be made in FF but would need someone that takes much time to build a script that could make this kind of complex maths and knows really much about this complex maths theory.

Righty. It gets so complex (no pun intended) the question becomes whether it is worth the time and trouble, when there are programs that already do this.

I am of the opinion it might be better to try and achieve something adequately similar without having to script it.

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Computer says "Yes!"

I say "Hell yeah!"

Way to go ThreeDee, you're still the master
Can you use any existing tileable texture with it, and show us an example?

Here's the construction of this pattern in visual form.

Take an upwrapped (unspherized) sphere with four quadrants.

Take the perimeter of the circle (the bottom line) and split in in three in each quadrant.

Draw overlapping circles centered on the meeting point of the perimeter and the lines that divide it into quadrants that go through these three splitting points.

Divide the resulting 12 sections of the perimeter into three.

In the same way draw circles that match these new points.

Repeat as many times as you deem necessary.

Spherize the result and behold hyperbolic tiling!

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Since unspherized hyperbolic lines are not actually circles, you get some distortion which you have to deal with, but that is a smaller issue.

This method can be improved upon in various ways, but this is the basic idea.

Wow great job!!

WELL WELL WELL what do we have here