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Author Topic:  I need a custom zoom into the logistic map for a short documentary  (Read 1024 times)

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Offline Fraktalist

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Hi guys!
I'm working on the follow up of our first short fractal documentary https://www.youtube.com/watch?v=tN_eNQFcv5E
The topic is roughly how the tree of life, evolution is a big fractal.
For one segment we need a (preferrable 1080p) zoom into the logistic map, like this:
But to a different location, with different speeds, maybe a zoom back out and then back into another location.
Is there any software out there that I can do this (without having to spend tooo much time to understand the software?
Or even better, would you be interested in helping out this project and create such a zoom for us?

Cheers,
Fraktalist

Linkback: https://fractalforums.org/index.php?topic=2062.0
« Last Edit: October 30, 2018, 10:57:18 AM by Fraktalist »


Offline Fraktalist

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Re: I need a custom zoom into the logistic map for a short documentary
« Reply #2 on: October 29, 2018, 11:35:40 AM »
thanks adam!
so it's possible - but those are very advanced programs with python knowledge required or manually writing the formulas. far beyond my capabilities and too much new to lean to achieve a short animation..
I hope there is an easier way, or someone is interested in helping me with that animation. Basically I want to zoom not into the middle, but show the branching 1-2-4-8-16...... until infinity and a first 'startover' at 1-2-4.....

Offline claude

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Re: I need a custom zoom into the logistic map for a short documentary
« Reply #3 on: October 29, 2018, 12:09:27 PM »
a first 'startover' at 1-2-4.....

I think you mean 3-6-12-24...

Offline Fraktalist

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Re: I need a custom zoom into the logistic map for a short documentary
« Reply #4 on: October 29, 2018, 02:13:33 PM »
hm, wasn't even aware of that.. damn, so deep into the rabbit hole and still so much to learn and obvious stuff I'm missing..

Offline claude

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Re: I need a custom zoom into the logistic map for a short documentary
« Reply #5 on: October 29, 2018, 02:32:20 PM »
It is related to the Mandelbrot set:


Offline Fraktalist

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Re: I need a custom zoom into the logistic map for a short documentary
« Reply #6 on: October 29, 2018, 08:24:05 PM »
yeah, know and love that fact already.
it's basically a 'lower dimension' or simplified display of what is happening in the branching of the mandelbrot set.
(correct me if I'm wrong or formulate things wrong please!)
also the reason for my thread a while back, asking if there is a trifurcation or n-furcation diagram as well..

do you know if the concept of shapestacking in the mset has some parallels in the bifurcation diagram?

Offline claude

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Re: I need a custom zoom into the logistic map for a short documentary
« Reply #7 on: October 29, 2018, 08:40:53 PM »
It's like a hybrid of the (anti plus regular) Buddhabrot (which displays outcome Z's) and the Mandelbrot set (which displays outcome for each C) - the whole thing is 4D (and has a name I'm not sure of, maybe "Buddhagram"), but the real/real slice is 2D, which can be displayed conveniently.

I think I replied to the n-furcation thread with some "rainbow fireworks" images...

I would guess the shape stacking applies, but it may be hard to see - in the real slice you can only stack needles (antenna tip) and cauliflowers (elephant valley), and cauliflowers don't have any details on the real axis... so not so interesting...

Offline claude

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Re: I need a custom zoom into the logistic map for a short documentary
« Reply #8 on: October 30, 2018, 01:17:40 AM »
Or even better, would you be interested in helping out this project and create such a zoom for us?

I might be up for helping a bit.  Post a storyboard (coordinates of key frames, duration between adjacent key frames, desired animation speed curve description, desired frame resolution, desired frame rate, desired colour scheme, any extras like labels or text).  I guess there will be narration, so maybe record the audio first to work out the timings?

I quickly coded up a bifurcation renderer, it's only 128 lines of code including comments to generate the looping animation attached.

I used the 2 Feigenbaum constants for the zoom speeds in 'a' and 'x', the coordinates of the first period doubling cascade limit as 'a' center of zoom, and the critical point 0.5 as the 'x' center of zoom.

2m25s render time for 64 frames at 640x360, so not too slow as to be infeasible.

Could do with an increased warm-up iteration count to reduce blurring near the parabolic branch points, and maybe motion blur to reduce strobing on the left hand side.  Just a first iteration...

Offline Fraktalist

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Re: I need a custom zoom into the logistic map for a short documentary
« Reply #9 on: October 30, 2018, 10:51:47 AM »
that's absolutely awesome claude!!!
Exactly what I was looking for!  :yes:
Very happy.

I quickly coded up a bifurcation renderer, it's only 128 lines of code including comments to generate the looping animation attached.
Wow. You keep surprising me.
We're in the early stage of preparation, no proper storyboard yet, we're going to meet in december/january for 10 days of full-time production.
I just posted this so early on because who knows how long this takes - I didn't expect a turnback time of 2 days..  :o :D
I'll let you know as soon as I can.
But quick thought: I guess the best thing would be to do a relativly slow, constant zoom and adjust the tempo dynamically in after effects. also adding text and stuff will happen there.

basically the goal is to use the bifurcation diagram as simplified model for the tree of life, with the repeating windows of order (starting over) as the development of a new species or even new stage of complexity (atoms->molecules->dna->single cells->multi cell organism->complex animals->intelligent life->technology->global brain internet 
See the attached image as a rough draft (first iteration also ;)


ps: not saying that the universe is this way, but our goal is to get people thinking about the surprising parallels and draw their own conclusions.
I find the bifurcation diagram and m-set are a great, simplified model for the far more complex and harder to grasp higher dimensional fractal that we imho live in and call reality.

Offline claude

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Re: I need a custom zoom into the logistic map for a short documentary
« Reply #10 on: November 01, 2018, 01:50:46 AM »
Here's one with 10 keyframes interpolated using PoincarĂ© half-plane metric for smooth zoom and sine ease-in/ease-out.  Squashed to 4 colours to be small in size.
https://mathr.co.uk/blog/2011-12-26_poincare_half-plane_metric_for_zoom_animation.html

BTW, this is plotting x against r in x := r x (1 - x) (logistic map representation)
Maybe you prefer plotting x against c in x := x^2 - c, so the shapes (at the top level especially) line up with the Mandelbrot set?


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