Shop Forum More Submit  Join Login
M.C.Escher Circle Limit III in a rectangle by Vladimir-Bulatov M.C.Escher Circle Limit III in a rectangle by Vladimir-Bulatov
Circle Limit III with fractal boundary and rectangular limit
Add a Comment:
 
:icondark-beam:
dark-beam Featured By Owner Apr 21, 2012  Student Artist
You are too smart! :nod:
Reply
:iconoaken-shield:
Oaken-shield Featured By Owner Apr 8, 2012
Really great stuff!
Reply
:iconz0k:
z0k Featured By Owner Mar 31, 2012
Would it be ok for me to use this for a while on my facebook page?
Reply
:iconvladimir-bulatov:
Vladimir-Bulatov Featured By Owner Apr 2, 2012  Professional General Artist
Yes, it would be OK.
Some form of credit would be appreciated :)
Reply
:iconann-mclaren:
Ann-McLaren Featured By Owner Jan 29, 2012  Hobbyist General Artist
Your deviation has been featured in my journal this week. [link] :hug:
Reply
:iconvladimir-bulatov:
Vladimir-Bulatov Featured By Owner Jan 29, 2012  Professional General Artist
Thank you!
Reply
:iconann-mclaren:
Ann-McLaren Featured By Owner Jan 30, 2012  Hobbyist General Artist
You are very welcome.:hug:
Reply
:iconshaylynnann:
ShaylynnAnn Featured By Owner Jan 28, 2012  Student Traditional Artist
Wow. I wish I knew the math behind this, I have a hard enough time with the circular poincare disk! Is this hyperbolic or fractal?
Reply
:iconvladimir-bulatov:
Vladimir-Bulatov Featured By Owner Jan 28, 2012  Professional General Artist
The math is based on Moebius transformations in complex plane.
They are genuine 3D hyperbolic transformation in 3D hyperbolic space but
observed on the boundary of the Poincare ball (analog of Poincare disk
for 3D hyperbolic space). The boundary of Poincare ball is projected
onto plane via stereographic projection.
So all the fishes are identical as they are in original Poincare disc view
in M.C.Escher woodcut.
Reply
:iconhop41:
Hop41 Featured By Owner Jan 27, 2012
Looks like it has 180 degree rotational symmetry?

I had thought it was circles intersecting the rectangle boundary at 90 degrees, somewhat like a poincare disk. But the big "circles" in the lower right and upper left look decidedly elliptical.
Reply
:iconvladimir-bulatov:
Vladimir-Bulatov Featured By Owner Jan 28, 2012  Professional General Artist
All circles were originally circles, but after conformal mapping (Mercator projection) they were a little squashed.
Reply
Add a Comment:
 
×




Details

Submitted on
January 27, 2012
Image Size
5.8 MB
Resolution
2250×1500
Link
Thumb

Stats

Views
4,299
Favourites
21 (who?)
Comments
11
Downloads
718

License

Creative Commons License
Some rights reserved. This work is licensed under a
Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.