Quaternion "Inside Views"

  • 17 Replies
  • 624 Views

0 Members and 1 Guest are viewing this topic.

Offline Kalter Rauch

  • *
  • Fractal Feline
  • **
  • Posts: 197
« on: December 11, 2017, 07:38:35 PM »
I've seen some extremely detailed M3D examples.
The obstacle has been getting only a nearly featureless display.
This turned out to be due to the front clipping plane.
After some manual adjustments I was able to get parts of this inside-out region
that could be zoomed into.
Then, after counterintuitively applying an inversion transform
I was able to render a complete object which could be studied
without clippng problems of which this is a closeup...





Linkback: https://fractalforums.org/chaospro/56/quaternion-inside-views/588/

Offline Kalter Rauch

  • *
  • Fractal Feline
  • **
  • Posts: 197
« Reply #1 on: December 11, 2017, 07:41:52 PM »

Offline Kalter Rauch

  • *
  • Fractal Feline
  • **
  • Posts: 197
« Reply #2 on: December 11, 2017, 07:43:04 PM »

Offline Kalter Rauch

  • *
  • Fractal Feline
  • **
  • Posts: 197
« Reply #3 on: December 30, 2017, 10:28:18 PM »
I think "Involution" is the correct term for this inside-out view of a Mandel/Julia bulb, etc.
By adding an inversion transformation the entire object can be seen,
otherwise zooming out becomes increasingly obstructed by intractable clipping plane errors.
Also, powers below 5 need separate parameters to work right.


Offline Kalter Rauch

  • *
  • Fractal Feline
  • **
  • Posts: 197
« Reply #4 on: December 30, 2017, 10:33:00 PM »
________________
« Last Edit: January 03, 2018, 03:16:39 AM by Kalter Rauch »

Offline Kalter Rauch

  • *
  • Fractal Feline
  • **
  • Posts: 197
« Reply #5 on: December 30, 2017, 10:34:52 PM »

Offline Kalter Rauch

  • *
  • Fractal Feline
  • **
  • Posts: 197
« Reply #6 on: January 03, 2018, 03:19:36 AM »

Offline Kalter Rauch

  • *
  • Fractal Feline
  • **
  • Posts: 197
« Reply #7 on: January 03, 2018, 03:22:19 AM »

Offline Kalter Rauch

  • *
  • Fractal Feline
  • **
  • Posts: 197
« Reply #8 on: January 03, 2018, 03:29:40 AM »
Here the foreground object is a composite of 2 involutions
while the background is one of another...


Offline Kalter Rauch

  • *
  • Fractal Feline
  • **
  • Posts: 197
« Reply #9 on: January 19, 2018, 09:58:15 PM »
3rd power Juliabulb Involution...


Offline Kalter Rauch

  • *
  • Fractal Feline
  • **
  • Posts: 197
« Reply #10 on: January 19, 2018, 10:02:15 PM »
4th power Juliabulb Involution/Joukowski transform...


Offline Kalter Rauch

  • *
  • Fractal Feline
  • **
  • Posts: 197
« Reply #11 on: January 19, 2018, 10:05:02 PM »
same as above...


Offline Kalter Rauch

  • *
  • Fractal Feline
  • **
  • Posts: 197
« Reply #12 on: January 19, 2018, 10:07:52 PM »
6th power Mandelbulb Involution...


Offline Kalter Rauch

  • *
  • Fractal Feline
  • **
  • Posts: 197
« Reply #13 on: January 19, 2018, 10:09:17 PM »
same as above...


Offline Kalter Rauch

  • *
  • Fractal Feline
  • **
  • Posts: 197
« Reply #14 on: January 22, 2018, 10:42:48 PM »
11th power Mandelbulb Involution...
By applying an inversion transformation
it is paradoxically confined to a shape which can be fully contained and studied......