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

 Pages: [1]   Go Down
 Author Topic: Classic Mandelbrot Set in 3D GIF animations  (Read 2370 times) Description: 0 Members and 1 Guest are viewing this topic.
in4ur
Forums Freshman

Posts: 10

 « on: September 09, 2014, 10:17:49 PM »

When I found an algorithm to extend the boundaries of the classic Mandelbrot Set to a third dimension, decided to create stereo images to enjoy the best 3D experience on a 3D TV, Oculus Rift or similar equipment. But... not many people can view images that way.

Recently, some users’ videos and animations made me think about how to show –a kind of– depth on any screen. Finally, I’ve made GIF animations moving smoothly (for more visual information) the “camera” position over the Set. It isn’t a true 3D experience like viewing side-by-side stereo images but, at least, shows the adding of the Z-Axis.

Here are some examples:

Image center: -1.941640269078771 + 0.000602115080593i. Width (real part): 3E-12

Typical Mandelbrot scene centered at 0.265023998510935 - 0.003027471362988i. Width (real part): 8.05872E-10

It can also be applied to Julia Sets (or any time-escape 2D fractal) like this. C = -0.7813 + 0.159i

 Logged
bib
Global Moderator
Fractal Senior

Posts: 2070

At the borders...

 « Reply #1 on: September 09, 2014, 10:47:36 PM »

Lovely effect, very intriguing!
 Logged

Between order and disorder reigns a delicious moment. (Paul Valéry)
Syntopia
Fractal Molossus

Posts: 681

 « Reply #2 on: September 09, 2014, 10:50:08 PM »

Looks great - I haven't seen anything like these before.

I imagine the depth is based on a smoothened escape radius, or something similar, but how do you render these things and how fast is it? Are they truly 3D, or does this only work for small camera deviations?
 Logged
cKleinhuis
Fractal Senior

Posts: 7044

formerly known as 'Trifox'

 « Reply #3 on: September 09, 2014, 11:22:35 PM »

i like the effect and the idea behind it very much as well, can you elaborate more what you do ? i think you apply an horizontal offset to the iteration bands after the image is completed, how do you avoid black-banding e.g. when one band is moved to far and space is created between 2 bands? or do you make it in a way of a depth texture that is warped in a post process ?
 Logged

---

divide and conquer - iterate and rule - chaos is No random!
cKleinhuis
Fractal Senior

Posts: 7044

formerly known as 'Trifox'

 « Reply #4 on: September 09, 2014, 11:23:17 PM »

i think this effect would benefit from a circular instead of a just horizontal movement
 Logged

---

divide and conquer - iterate and rule - chaos is No random!
3dickulus
Global Moderator
Fractal Senior

Posts: 1558

 « Reply #5 on: September 09, 2014, 11:35:26 PM »

wow, I know its 2D but my brain says it's 3D    reminds me of the effect of not enough sleep and too much hacking
 Logged

Resistance is fertile...
You will be illuminated!

#B^] https://en.wikibooks.org/wiki/Fractals/fragmentarium
KRAFTWERK
Global Moderator
Fractal Senior

Posts: 1439

Virtual Surreality

 « Reply #6 on: September 10, 2014, 08:44:30 AM »

WOW!

I'd love to 3D print that second one as a "shell", would be nice to see how those spirals looks on the "backside"...

Is it possible to export as a voxel-stack or mesh as 3D? ...or is it only a "constructed" 3D effect?
 Logged

cKleinhuis
Fractal Senior

Posts: 7044

formerly known as 'Trifox'

 « Reply #7 on: September 10, 2014, 09:07:31 AM »

he seems to use the iteration bands as separated layers and moves them according to the iteration depth ... i think the effect could be created with a normal frctal rendering software to get the slices, just increase the iteration count in every slice, which should give you an eroded or deepened minibrot 3d prints with moving parts would be awesome

 Logged

---

divide and conquer - iterate and rule - chaos is No random!
Alef
Fractal Supremo

Posts: 1174

 « Reply #8 on: September 10, 2014, 04:45:15 PM »

Ha ha, nice. Some darkening in the insides would be more nice but movement too gives nice feel of 3D-ness.
 Logged

fractal catalisator
in4ur
Forums Freshman

Posts: 10

 « Reply #9 on: September 10, 2014, 08:08:18 PM »

Sorry for the delay in answering, but my English level doesn’t allow me to reply quickly and well (or attempting to do so) at the same time.

The idea of the 3D Mandelbrot rendering appeared as an answer to the questions: what if classic Mandelbrot is a 2D photo of a 3D landscape and the hidden axis is the escape time of each point? How would it look like if we see it from two points of view (the eyes) instead of one for a binocular vision of the Set and distance perception through parallax variations? This reflects in a “simple” and elegant algorithm (in my very subjective opinion ;-P) that calculates the view from a selected camera position and generates stereo images (http://www.flickr.com/photos/in4ur/) for a full and detailed 3D experience on the right equipment. I have created animated GIFs only as a way to introduce the effect to anyone on any screen.

The algorithm is a variation/ampliation of the standard time-escape procedure that adds and modifies (apart from variable declarations) 10-15 lines of code. There is no post-processing at all and the calculation is done by a less_than_80_lines_of_code C routine, including the creation and recording of the resulting image on a BMP file; just because is one of the easiest image formats. The only “special feature” is supersampling 4x4 to reduce noise.

Each stereo image or frame takes around 10 times the time required to calculate a classic Mandelbrot one, but depends on the parameters values. The method has some similarities with ray-tracing and applies to points and pixels. The resulting iteration bands for each point of view are a consequence of the calculations with the pixels. I don’t think the moving bands approach would work. The bands have to modify their shape according with the perspective, the mentioned black-banding issue... Ufff!

Is it truly 3D? Good question. If you look at a strange landscape through a window, are you viewing it in 3D? You perceive parallax, distances and the 3D shapes of the visible parts of the objects, but you can’t create complete 3D models of them due to the lack of information. The same occurs with the 3D extension of the Mandelbrot Set. I can calculate exactly or almost exactly how it looks in 3D for small deviations like interocular distances or even moderate ones, but from big deviations you see zones that are “behind” the Mandelbrot Set and the principles in which the 3D extension is based do not provide information about “what’s there”; you have to guess. The algorithm does a good job guessing by simply applying to the unknown the procedure that works with the known, but it doesn’t make miracles. You need more assumptions if you want to complete the model.
 Logged
Chillheimer
Global Moderator
Fractal Schemer

Posts: 972

Just another fractal being floating by..

 « Reply #10 on: September 10, 2014, 10:40:08 PM »

yeah!
this looks great!
incredible work.. just 10-15 lines of code? wow.

pleeeeaase, go ahed and share the code with kalle so this finds it's way into a (open source) tool that uses pertubation method!
http://www.fractalforums.com/kalles-fraktaler/
this would be so cool in there.. actually it would be a reason to buy an occulus rift for me.. finally really immerse into the mset...
 Logged

--- Fractals - add some Chaos to your life and put the world in order. ---
bib
Global Moderator
Fractal Senior

Posts: 2070

At the borders...

 « Reply #11 on: September 10, 2014, 10:49:13 PM »

WOW!

I'd love to 3D print that second one as a "shell", would be nice to see how those spirals looks on the "backside"...

Is it possible to export as a voxel-stack or mesh as 3D? ...or is it only a "constructed" 3D effect?

My 2 cents: with M3D animation mode in 2D, integer power 2, just changing iteration count between 2 keyframes and with an appropriate B&W color gradient that should be doable to get a nice voxel stack...
 Logged

Between order and disorder reigns a delicious moment. (Paul Valéry)
cKleinhuis
Fractal Senior

Posts: 7044

formerly known as 'Trifox'

 « Reply #12 on: September 10, 2014, 11:31:02 PM »

use a 2d fractal explorer for rendering, having finer control over color/iteration, but mb3d would suite as well, right, outsidecolor=white, increase iteration for each layer - BUT - better use a smooth coloring, to get a super fine gradient, and then, make 10 layers and place them in a moveable cube so that each layer may be moved for its own
 Logged

---

divide and conquer - iterate and rule - chaos is No random!
in4ur
Forums Freshman

Posts: 10

 « Reply #13 on: September 12, 2014, 10:00:21 PM »

yeah!
this looks great!
incredible work.. just 10-15 lines of code? wow.

pleeeeaase, go ahed and share the code with kalle so this finds it's way into a (open source) tool that uses pertubation method!
http://www.fractalforums.com/kalles-fraktaler/
this would be so cool in there.. actually it would be a reason to buy an occulus rift for me.. finally really immerse into the mset...

I don’t know what I’ll do.

I’d love to program an Oculus Rift fractal navigator myself, though I’ll have very limited free time in the next months/year and there is a lot to learn about the SDK. Other options are to find someone to collaborate with or, simply, share and publish (somehow) the algorithm and explain how and why it works, which requires more lines than the code itself.

PS. The second development kit for the Oculus Rift is available now. A consumer version of the VR headset is expected by the end of 2015.
 Logged
thargor6
Fractal Molossus

Posts: 789

 « Reply #14 on: September 12, 2014, 10:19:12 PM »

simple, but really nice effect, love it :-)
 Logged
 Pages: [1]   Go Down