Logo by DsyneGrafix - 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: Did you know ? you can use LaTex inside Postings on fractalforums.com!
 
*
Welcome, Guest. Please login or register. March 28, 2024, 09:48:27 PM


Login with username, password and session length


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



 
  Search  

  Slideshow  
flying duckelephantmandel3d
elephant
Previous Image | Next Image
Description: next attempt, like in wonderful mandelbulb, angles are measured, theta around the equator, phi through the poles. phi is measured in multiples(or parts) of pi, the respective value afterwards squared. Theta is doubled. z1 is determined as a point in a coordinate system, theta along the x-axis, phi along y-axis. the distance from zero on the z-axis, in logarithmic scale. the unit sphere will be mapped onto a rectanglenear the origin. the mandelbulb algo is done by choosing a point on the equator, from this point doubling the distance to any point z1, so we will reach z2. Taking the point on the line, which is representing the north-pole, we will get algorithms (similar to the squaring of quaternions,), they are implemented in T. Gintz´s Quasz as "gedatou" and "ventri".(Squaring quaternions is done by doubling phi, measured from the pole, theta remaining unchanged. We can imagine a rubber-ribbon around the equator. Measuring phi from it, we get mandelbulb("rings of fire" in Quasz-but only for power 2), sliding the ribbon to the north-pole, the mandelbulb-algo will change to "gedatou"(if the ribbon is shrinked to one point on the line, representing the pole, if the ribbon is extended along this pole-line, it will change to the squaring of quaternions, so we may see the connection between squaring of quaternions and hypercomplex numbers). Using this coordinate system, we get a certain freedom to develop new algorithms, even sometimes preserving the mandelbrot set in one plane. In this picture still same angles phi are mapped to points with same angles phi2, maybe we could change this to get more harmonic structures in all(?) directions?  
Stats:
Total Favorities: 0 View Who Favorited
Filesize: 89.19kB
Height: 675 Width: 1264
Keywords: mandelbrot set threedimensional 3d   mandelbulb gedatou ventri rings of fire 
Posted by: vector January 03, 2010, 08:31:59 PM

Rating: ***** by 3 members.

Image Linking Codes
BB Code
Direct Link
Html Link
0 Members and 1 Guest are viewing this picture.
Related Images
Elephant Talk


Rating: *****
Filesize: 737.04kB
Date: July 19, 2010, 10:19:42 PM
Comments (1)
By: hermann
Classic elephant valley minibrot - revisited


Rating: *****
Filesize: 886.61kB
Date: September 11, 2010, 09:51:50 AM
Comments (9)
By: bib
Elephant Talk


Rating: *****
Filesize: 4.44MB
Date: April 04, 2016, 05:58:44 PM
Comments (2)
By: Fractalisman
White Elephant


Rating: *****
Filesize: 1006.83kB
Date: April 09, 2016, 12:42:38 AM
Comments (9)
By: floppyHat
Elephant


Rating: *****
Filesize: 3.04MB
Date: November 10, 2016, 11:37:21 PM
Comments (4)
By: Sabine
  Slideshow  

Comments (2) rss
vector
Forums Freshman
**
Posts: 14


View Profile
January 07, 2010, 09:34:19 AM
okay, hen or chicken might be more suitable, but i thought the mass of the corpus(often the mandelbrot sets are somehow flattened, using loxodromic functions or related algorithms) and the spiralic trunk-like structure below at the right,and to remember it one year later, i preferred to memorize elephant more than hen.
bib
Global Moderator
Fractal Senior
******
Posts: 2070


At the borders...


View Profile WWW
January 05, 2010, 11:09:32 PM
Interesting! But where do you see an elephant? I can see a flying hen maybe smiley

Return to Gallery

Powered by SMF Gallery Pro

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 0.21 seconds with 33 queries. (Pretty URLs adds 0.006s, 1q)