Logo by S Nelson - Contribute your own Logo!

END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval,
thanks and see you perhaps in 10 years again

this forum will stay online for reference
News: Follow us on Twitter
 
*
Welcome, Guest. Please login or register. March 29, 2024, 09:02:30 AM


Login with username, password and session length


The All New FractalForums is now in Public Beta Testing! Visit FractalForums.org and check it out!


Pages: 1 [2]   Go Down
  Print  
Share this topic on DiggShare this topic on FacebookShare this topic on GoogleShare this topic on RedditShare this topic on StumbleUponShare this topic on Twitter
Author Topic: Why there isn't 3D 1:2 conformal transformation?  (Read 1072 times)
0 Members and 1 Guest are viewing this topic.
Roquen
Iterator
*
Posts: 180


« Reply #15 on: September 20, 2013, 11:10:14 AM »

Facepalm. I see my logic error. In case anyone in the future persists to attempt to poke a hole, let me attempt an explanation.  Sticking to R3, using my proposed construction the resulting space is identical R3 so 'f' is restricted to Liouville's.  Attempting to define a conformal "except" some subspace the same holds.  Take "except some plane", then the subspace on the positive side excluding the plane is conformal only of 'f' is Liouville's.  The same holds for the negative side.  Shrink the plane to a line then the two sides except the line must have the same 'f' to be conformal except the line.  The same holds for any choice of "except" subspace(s).  So any analytic function 'f' is either Liouville's or nowhere conformal.
Logged

All code submitted by me is in the public domain. (http://unlicense.org/)
Alef
Fractal Supremo
*****
Posts: 1174



WWW
« Reply #16 on: September 25, 2013, 03:45:11 PM »

Well, then no grails so far. Throught probably using alredy known transformations in more exotic spaces like hyperbolic space could result in something new. Or maybe not.

Comment claims ";This produces slice of the second order Mandelbulb directly perpendicular to the regular Mandelbrot set." Simple  cutout  of sine pow2 mandelbulb in y=0 plane:
z=z^2+c
z= abs(real(z))- 1i*(imag(z))

Cosine pow 2 mandelbulb in y=0 cutout looks lika mandelbrot set with slightly different reflection.
So mysterious mandelbulb too are demistified, mundelbulb formula just involves reflection.

However "The Rudy Rucker's formula for 3D Mandelbrot of 1991 year", a "Ruckerbulb" in perpendicular cutout generates something more like real mandelbrot, but then it have a lot of noise.

http://www.fractalforums.com/new-theories-and-research/complex-not-so-complex/msg61882/#msg61882





* mb_cosine_pow2_bulb_perpendicular_cutout.jpg (31.85 KB, 480x360 - viewed 112 times.)

* mb_Rucker_pow2_bulb_perpendicular_cutout.jpg (39.17 KB, 480x360 - viewed 113 times.)

* mb_sine_pow2_bulb_perpendicular_cutout.jpg (42.97 KB, 480x360 - viewed 118 times.)
« Last Edit: September 25, 2013, 03:46:43 PM by Alef » Logged

fractal catalisator
Pages: 1 [2]   Go Down
  Print  
 
Jump to:  

Related Topics
Subject Started by Replies Views Last post
Special Conformal Transformations of Conformal Geometry General Discussion rloldershaw 7 7858 Last post April 22, 2015, 08:26:04 PM
by DarkBeam
Continuous Conformal Mandelbrots Amazing Box, Amazing Surf and variations « 1 2 » Tglad 21 19670 Last post September 11, 2012, 01:16:06 PM
by ericruijun
Another take on Conformal Transforms (new) Theories & Research hobold 12 725 Last post August 25, 2012, 08:52:24 PM
by weshoke
2d/3d conformal formulas for a tetrahedral projection Mandelbrot The 3D Mandelbulb « 1 2 ... 5 6 » Tglad 85 46721 Last post September 10, 2015, 08:42:50 AM
by pupukuusikko
Conformal mapping Mandelbulb 3d ericr 6 3075 Last post February 29, 2016, 04:44:38 PM
by ericr

Powered by MySQL Powered by PHP Powered by SMF 1.1.21 | SMF © 2015, Simple Machines

Valid XHTML 1.0! Valid CSS! Dilber MC Theme by HarzeM
Page created in 0.15 seconds with 24 queries. (Pretty URLs adds 0.007s, 2q)