Calcyman's Idea (2D)

[stigomaster]

Nice, "free" is my favorite price. 

Is it also open source?  I'd be more than willing to contribute to the project, if so.

ChaosPro is unfortunately not open source, just freeware. And it's Windows-only, but it runs well in Wine. 

[kram1032]

LesPauls: Which powers are included? It looks nice

[LesPaul]

LesPauls: Which powers are included? It looks nice

Thanks!  I want to experiment more, both with the formula and the video codec settings to try to make it cleaner.  I did a version with no compression but it came out to about 400MB and YouTube probably wouldn't be happy about that. 

The power goes from 2.0 to 1.0, so the first frame is exactly

  z_n+1 = z_n² * tan(z_n) + z₀

and the last frame is exactly

  z_n+1 = z_n * tan(z_n) + z₀

The power-2 version behaves very nicely but the power-1 version does not.  I'll make a video that zooms out as the power decreases and it will show how the whole thing basically blows up when the power becomes 1.

[LesPaul]

A related question - Is there any particular software that you guys use for your video editing?  I'd really like to be able to just render the animation to individual frames (PNG) and then play around with different levels of compression.

[LesPaul]

The power-2 version behaves very nicely but the power-1 version does not.  I'll make a video that zooms out as the power decreases and it will show how the whole thing basically blows up when the power becomes 1.

Here it is.
<a href="http://www.youtube.com/v/HHDOqBfdO_Y&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/HHDOqBfdO_Y&rel=1&fs=1&hd=1</a>

[Nahee_Enterprises]

A related question - Is there any particular software that you guys use for your video editing?  
I'd really like to be able to just render the animation to individual frames....

Have you tried VirtualDub ??  It is FREE !!!!    

You might also be interested in the FREE K-Lite Codec Pack, which comes in various downloads:

• Basic
• Standard
• Full
• Mega
• Corporate
• 64-bit

[David Makin]

A related question - Is there any particular software that you guys use for your video editing?  
I'd really like to be able to just render the animation to individual frames....

Have you tried VirtualDub ??  It is FREE !!!!   

I use VirtualDub and the Xvid codec - *both* free

[bib]

Hi
Another vid using the formula  z=z^n*tan(z)+c

<a href="http://www.youtube.com/v/ToWAOKeNKXw&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/ToWAOKeNKXw&rel=1&fs=1&hd=1</a>

[kram1032]

whoa, that's a great zoom and value-shift

[LesPaul]

Wow, fantastic, bib!

I thought for sure that there was going to be a minibrot at the end of the zoom. 

Several places in z*tan(z) that I've roamed around and zoomed have revealed minibrots.

[LesPaul]

I just noticed that at 1:17 in bib's video, two minibrots "float" across the chaos from right to left...  It's very unusual, because they aren't classical minibrots in the sense that they don't appear to actually be inside the set.  The chaotic background noise appears to shape itself into minibrots.  I've definitely never seen that before.  z*tan(z) is such an unusual set.

[Timeroot]

I had actually noticed that too. Due to the high level of noise present and the unusual inside coloring, it's hard to say whether or not these minibrots are inside the set. But I'm not the one to know things here...   It is a strange beast indeed.

[Calcyman]

On one of the first images of this fractal set, it is possible to see Mandelbrot-shaped formations with internal substructure. In other words, those formations are not actually part of the Fatou set of the function. Rather, it appears that crossing the border into these curiosities is like passing through an asymptote -- something which seems quite possible given the nature of the tangent function.

Indeed, the first picture (courtesy of Bib) displays this artefact really clearly. The inside of this bubble-like anomaly is populated with fractal swirls, which contrasts with the globular clusters outside the anomaly. Minibrots bridge the gap between these worlds, as if unperturbed by the asymptote.



This can also be seen in LesPaul's second image, albeit less clearly.

Maybe we should translate this series back into triplex, and see if it yields the elusive "True 3D Mandelbrot".


What about z = tan(z)^2 + c? That might be even more remarkable than the hybrid form (z*tan(z) + c). It's certainly simpler and more elegant in definition.

[bib]

These kinds of shadow buds is something I have been looking for in other fractals, like in these pics. I don't know the details of the maths behind unfortunately, but I guess that they have in common to diverge for some real values (e.g 1/(1-x) or tan(x))

[kram1032]

tan delivers some of the most beautiful sets, really O.o