Hyperbolic Tiling Challenge

Quote
Uberzev wrote: If I can understand the pattern in which the arcs are placed and sized I can make an efficient FF version. What I've been doing is manually position everything.

Unfortunately it is not a repeating pattern other than around the symmetry axes of the center polygon. You would have to calculate every arc size and location with a script in any case. It seems to me after some study of the math behind proper hyperbolic tiling that uniform tiling (equal corner angle hyperbolic polygons) would require a recursive calculation for each subsequent arc once you know the previous one.

That is where I gave up on accuracy and settled for visual similarity.

I have managed to get the input image to (sort of) tile in this nonuniform hyperbolic tiling now.

It is anything but optimized or accurate, but probably as close as I will ever have the patience to get it.

WOW!! This is really great and beautiful ThreeDee, very well done.

Quote
uberzev wrote: heh, that image wasn't made with FF. There's a simple windows program for making hyperbolic tiles

Thanks for the link is very interesting and useful

Here SR...
http://www.filterforge.com/filters/1762.html

You may need to flip your image vertical first.

Thanks uberzev and Skybase, but I have tried all the unspherize and spherize filters available in FF and also the polar coordinates ones from FF and the one from Photoshop AND I am sorry to tell that I must be dumb because I have not been able to make the conversion from the straight line to the round lines.

I have made this right with a very basic color line to make a target like using any of this filters, BUT you convert the colors to real shapes they get very distorted and loose much the original shape and does not look at all as the very good examples shown. And I tried it with vertical rotation.

Will have to search in Google how to convert 2D line to a circle in " Convert for dummies"

ThreeDee,It is not a hyperbolic tiling.
A "Line" in Poincaré disk model must be a segment of a circle or a diameters of Poincaré disk.
A curve made by above way is not a circle in x-y plane, so this curve is not a "line" in Poincare disk.

Hi Inujima,

Yes, I know, that described method gives you something resembling hyperbolic tiling that you have to distort by Curve and Lookup components (either before or after spherizing) to make them segments of a circle. You can output "proper" hyperbolic tiling with it if you do so. The limitation is that it is not regular tiling, meaning the tiles are not hyperbolic polygons with equal corner angles, just hyperbolic polygons.

It definitely requires scripting to get the accurate position of the circles if you want to make regular tiling, for the reason you stated.

Quote
distort by Curve and Lookup components (either before or after spherizing) to make them segments of a circle.

I say it is impossible to make circle segments from any half circles in polar coordinate by this way.
If one half circle goes to a circle segment, then other half circle having different radius will not go to a circle segment.

Scripting is cheating..

Nice job though.

2.0からいろいろと自分で試していたのですがやはりスクリプトにはかないませんね。犬島さん㭀ã™ã”いです！自分は使ったとしてもPythonかMelで単純作業用のスクリプトぐらいしか作れませ­ã‚“し、LUAなんて見てもなんかまだわからないことだらけで．．．．

Now I feel like I spoke engrish.

Engrish? I thought it was Japlish!

Excellent work, Inujima!

Skybase I have already seen this beautiful and great creations you have with Artmatic and I like them much, BUT regretably Artmatic is ONLY for Mac

WOW!!! Inujima, I can´t believe the awesome and amazing filter you have done !!!!! I am breathless and speechless

Love your filter and love you for having made this in such a perfect and excellent way !!!!

When this thread started I never imagined at all that the result could such a beauty and real gem as the one you have done here Inujima.

Thanks a million for making this fantastic filter!!!!

AND furthermore is fast TOO !!!

and even more closer detail to see how really perfect and how beautifully is made the fractal tiling into far far away

and here in more detail, like much how the fractal tiling is done that looks so well even on the tiny parts

This can have LOTS of possible and different combinations using just the same source and look different

Amazing scripting. I don't understand any of it.

BTW this image can be reproduced with 3, 4, 1 in the settings.

See the quality in more detail here

I take it back. It is not just excellent, it is incredible!

I am feeling quite escheresque already.

Quote
uberzev It is not just excellent, it is incredible!

I agree, Excellent is not enough, it is incredibly awesome and amazing

AND IT ALSO WORKS PERFECTLY WITH NON SQUARE IMAGES !!!

The clocks image here is really a rectangular photo BUT this filter does not care if it square or rectangular, it makes the tiling in the top part of the photo as it was square.

SO, this also open a much wider possibilities as ANY image can be used and it does have to be square to work right in this filter.

Here is the real result from the NON SQUARE image

and see more closer how excellent quality it brings on the tiling just adjusting a little the settings