### Inverse tree generation (escape-time like)

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• Posts: 171

#### Re: Inverse tree generation (escape-time like)

« Reply #15 on: October 03, 2018, 02:01:18 PM »
A fix? for the single sequence method:
If you accumulate a divergent matrix instead of transforming the point i.e. transform the original point at each stage using the accumulated divergent matrix and once you've got d+1 transforms combined (where d is the required depth in the original tree) undo the first by applying the inverse of the first in the accumulation to the accumulation then just the single point, the accumulated matrix and the original transforms and their inverses are required (plus temporary stuff) - only the accumulated matrix is required from loop to loop all the rest can be essentially hard coded.

Edit:
Also a simple (untested) algorithm for creating a reasonable sequence is at each stage check which transform added next gives the highest number of possible (not already covered) sequences of the required depth with itself last, another afterwards last another afterwards last etc. - this algorithm is independent of the required depth and number of transforms as long as all possibilities are counted.
More: The algorithm for creating the shortest sequence could also be modified to allow for different branches having different depths (i.e. the required sequences to include not necessarily all having the same number of transforms) - of course the render loop would also need to be modified to allow for this, I think it could still be managed without adding arrays or more dynamic matrices.
« Last Edit: October 04, 2018, 05:35:35 PM by FractalDave »
The meaning and purpose of life is to give life purpose and meaning.

#### msltoe

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#### Re: Inverse tree generation (escape-time like)

« Reply #16 on: October 05, 2018, 03:40:30 AM »
Inverse tree generation in 3D is slow. Distance estimation might help.

• 3f
• Posts: 1666

#### Re: Inverse tree generation (escape-time like)

« Reply #17 on: October 05, 2018, 03:53:24 AM »
Nice one. You can almost feel the fuzz.

#### Sabine62

• Fractal Frankfurter
• Posts: 624

#### Re: Inverse tree generation (escape-time like)

« Reply #18 on: October 05, 2018, 10:41:38 AM »
Ohh, this is Nice!
To thine own self be true

• Posts: 171

#### Re: Inverse tree generation (escape-time like)

« Reply #19 on: October 05, 2018, 03:02:18 PM »
Timings for recursive escape-time method in UF - (entirely on CPU):
Images 715*954 straight from UF except addition of Coloursync.

As implemented the basemodel hexagonal tube could be any primitive, in fact as written it's nowhere near optimum especially with respect to this.
Edit: That's because I was too lazy to code it up properly and did it just for proof of principle so the "basemodel" tube is actually an IFS itself - hence the rather slow render times...
« Last Edit: October 08, 2018, 01:39:44 PM by FractalDave »

• Posts: 76

#### Re: Inverse tree generation (escape-time like)

« Reply #20 on: October 05, 2018, 04:52:08 PM »
Inverse tree generation in 3D is slow. Distance estimation might help.
Thank you for doing the 3d experiment! The fuzziness is really cool; never before have I seen a 3D fractal carried out to such a high iteration depth. IMHO the overall impression of the object is significantly changed by that fuzz. Time to re-explore many old classics?

#### Alef

• Fractal Phenom
• Posts: 53
• catalisator of fractals

#### Re: Inverse tree generation (escape-time like)

« Reply #21 on: October 05, 2018, 05:22:54 PM »
Personaly the most I like rotated tree. Bu I think the best would be a spruce/fir tree. In generation it is very simmilar to fern, once I got christmas tree by modifying fern ifs. It have branches curved in just opposite direction. This is darwinian adaptation to snow. On curved branches of spruces or birches snow don't stayes, so tree don't need to carry so mutch snow.

OK, now this 3D is far from artistic. But I think this thing is quite a perspective. People prefare natural patterns they see in life.

Realy the last one seems to be close to christmas tree.
« Last Edit: October 05, 2018, 05:35:10 PM by Alef »
catalisator of fractals

#### msltoe

• Fractal Fanatic
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#### Re: Inverse tree generation (escape-time like)

« Reply #22 on: October 06, 2018, 02:10:00 AM »
Thanks for the compliments, everyone!

Hobold: Since I have never used accurate distance estimation in my codes, my renderings tend to be more fuzzy. My renderer normally marches through space at roughly 0.1 voxels/step looking for the viewable plane. It then backtracks a few times to an accuracy of 0.025 voxels. For the most recent picture, I set the initial step size to 0.25 voxels, to save time.

I think fuzziness is found a lot in tree fractals. I was also able early on to get fuzziness using an increasing power Mandelbulb, i.e. first iteration is power 2, next power 4, next power 6, etc. Once again, having a very fine step size helps.

One other point is that with tree fractals, it would be very challenging to get a lot of fuzz/hair with the forward method, because the number of primitives grows exponentially and would use up a lot of memory. The inverse variant is much more memory efficient only keeping track of the current recursion stack of visible search pointer. Maybe a hybrid of the two methods would strike the right balance of memory/speed?

#### mclarekin

• Fractal Frogurt
• Posts: 493

#### Re: Inverse tree generation (escape-time like)

« Reply #23 on: October 06, 2018, 03:10:52 AM »
I like the fuzziness tree.

the C code is at first glance, a  bit advanced for me.

On my wish list is trees that can be animated to music, and also  trees that grow

#### msltoe

• Fractal Fanatic
• Posts: 27

#### Re: Inverse tree generation (escape-time like)

« Reply #24 on: October 06, 2018, 05:39:15 AM »
I made a "fern" with a little more color.

• 3f
• Posts: 1666

#### Re: Inverse tree generation (escape-time like)

« Reply #25 on: October 06, 2018, 05:42:05 AM »
I made a "fern" with a little more color.
Really nice. I'd like to have it in higher resolution though.

#### Alef

• Fractal Phenom
• Posts: 53
• catalisator of fractals

#### Re: Inverse tree generation (escape-time like)

« Reply #26 on: October 06, 2018, 02:59:46 PM »
I made a "fern" with a little more color.
It's beautifull. It could be some trophical palms often grown in buildings (I don't know the name).

I think it could be extended to spruce trees just by curving branches in the opposite directions:

#### msltoe

• Fractal Fanatic
• Posts: 27

#### Re: Inverse tree generation (escape-time like)

« Reply #27 on: October 06, 2018, 05:16:09 PM »
Really nice. I'd like to have it in higher resolution though.
I'd like to get to higher res, too. It's actually a 1600x1600 render downsampled to 800x800 (+ crop) to get rid of some of the noise when the features get too small. The render took 2 hours on an 8-thread machine. So, a 3200x3200 with my current technique would take 16 hours.

#### msltoe

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#### Re: Inverse tree generation (escape-time like)

« Reply #28 on: October 07, 2018, 02:37:38 AM »
Fuzzy tree.

• 3f
• Posts: 1666

#### Re: Inverse tree generation (escape-time like)

« Reply #29 on: October 07, 2018, 06:01:01 AM »
Very nice. I want to eat it!

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