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Author Topic: Swirlbox 10 and a few zooms  (Read 1816 times)
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Alef
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« on: March 04, 2013, 06:45:32 PM »

Used animation keyframe spot of a video and then a bitt tweaked colours.

Far zoom out wiev shows pretty interestic owerall shape:





Then a bitt closer wiev so that folia like texture is more noticable:





Closer look on the central x,y=0 onion or cabbage like part of formula :





Square hole with piramid inside created by folding space with number of swirls:





Look down from the central piramid on a pattern simmilar like in 2D.

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Apophyster
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« Reply #1 on: March 05, 2013, 09:15:21 AM »

 Yes !! Your explorations are becoming quite interesting. Yes !!
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cKleinhuis
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« Reply #2 on: March 05, 2013, 11:21:33 AM »

nice pics, can you again write down the pseudo code formula, e.g. where did you put in the swirl operation ?
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Alef
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« Reply #3 on: March 06, 2013, 06:35:13 PM »

It didn't changed from this http://www.fractalforums.com/new-theories-and-research/swirlbox/
Swirl is done only after modified folding, "fish eye" rounding and scaling.
Throught exploring with some more advanced raytracer could lead to less rough pictures;)
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Alef
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« Reply #4 on: March 07, 2013, 04:33:53 PM »

Finnaly get to the bottom of zoom sequence.

Looks somewhat rough or battered throught.


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kram1032
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« Reply #5 on: March 07, 2013, 07:18:48 PM »

Now we're starting to talk. It's really becomming quite interesting!

Have you tried very sublte swirl factors? Like, with frequencies of a tenth, a hundreth, etc.?
It would be interesting to see how sensitive the shapes are to swirling.
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Alef
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« Reply #6 on: March 09, 2013, 01:25:29 PM »

Not shure, but I tried couple of factors, and it looks that something like from 4 to 8 generate the most interesting shapes. Some swirl parameter combinations generated cabbage / "butterfly curve" some other something like round mandelbox. But I think deep zooms are more interesting, treerings and astroids.

Zoomed into the upper left hole at the bottom of the pillar ( small light areas in picture above).

Of corse not without some post render blur, contrast, equalisation and colour tweaking.


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kram1032
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« Reply #7 on: March 09, 2013, 07:16:22 PM »

Another nice one. It gives you an obvious look at the "swirliness"

In other fractals, this might be considered whipped cream, but for this one it's actually what you'd expect: fractal repetition of swirls.
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Alef
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« Reply #8 on: March 15, 2013, 04:32:11 PM »

Zoomed further inside, up to the pillar of last picture. It should be mostly hollow inside. In certain in between regions it looks as innate

whiped cream or streched, but further away normal patterns appears. At least some  smooth surfaces should be artefact of light and AO,

as in far wievs some portion looks as having pronounced ring shapes, then on zooming in it looks flat. But on switching on some side

lights it regains holes.

Up to the pillar, finaly there are noticable swirls:





Zoom somewhere in the middle of the pillar. Attention grabed central hexagonal spot around whom pattern are organised, throught raytracing somewhat failed with plane being in angle:


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Eric B
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« Reply #9 on: March 15, 2013, 05:38:07 PM »

These are impressive. I especially like image 5956_15_03_13_4_08_02 (1)
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kram1032
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« Reply #10 on: March 16, 2013, 12:03:12 AM »

shapes in this one are way less well-defined compared to other fractals out there. In any case, though, they look nice.
It's certainly much harder to make out "types" of structures. - like, to define regions like on the MSet: "Seahorse valley" or "Elephant valley", etc.
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Alef
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« Reply #11 on: March 16, 2013, 02:43:36 PM »

Thanks. Swirls are assymetric so with folding it turnes extremely chaotic. Interesting feature is that it looks like cutted whet it is not.
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kram1032
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« Reply #12 on: March 16, 2013, 07:12:25 PM »

they do have certain kinds of assymetry. Just not the usual type.
This is why a logarithmic spiral might be more regular: It's scale free in that you can size it up arbitrarily and you will find a rotation in which it will fit the exact same way again.

The archimedan spiral, as used here, just keeps every rotation at the same distance, causing other behaviors.


If you want to use a logarithmic spiral, you need to change the angular part to:
\phi = b \arg{\left(x+\I y\right)} +\frac{c}{2} \log{\left(x^2+y^2\right)}
and the typical power, as always, would be z\mapsto \left(r^n,n \phi\right)+c

Can you try that? Just exchanging the angular part in your formula you have so far by this?
If I'm not mistaken, all you need to do is change a single \sqrt{\left(\,\right)} into a \frac{1}{2}\log{\left(\,\right)}.
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Alef
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« Reply #13 on: March 21, 2013, 05:49:26 PM »

Actualy angle part had fallen from haven;) I didn't put on the paper to check all the trigonometry, just tried all the variants till it generated expected result. So I 'm not shure about mathematical correctness of angles.


Zoomed further into generated curves right to the Cthulhu like figure. It seems that raytracing prefers  surface being parralel to screen, and but more it prefers stand alone objects. Else it is hard to get good contrast and smoothess at the same time. But assymetry is kind of cool.






And generated large scale julia set with almoust the same parameters as m-set. It's symmetric hedgehog/porcupine  and it should be generated by different version of spiral, seen  when cutted.  



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hgjf2
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« Reply #14 on: March 22, 2013, 08:42:03 AM »

Thanks. Swirls are assymetric so with folding it turnes extremely chaotic. Interesting feature is that it looks like cutted whet it is not.
Thanks ALEF. wink smiley A peacock Smiling Mandelbrot
I looked that you posted many anything at topic "2nd fractal annual competition (completed)" when can posting much at topic "image showcase" and the topic "mandelbulb software".
I want to know that do you join at a fractal competition?
« Last Edit: March 22, 2013, 08:45:22 AM by hgjf2 » Logged
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