Extension of "folding"

[David Makin]

Nope - am still "tweaking" - may take a few days as its (useful) potential just grows as I try each idea - so far everything I add produces some great additional potential *without* any large performance hits - it's quite refreshing, usually things you add are either fast but useless or brilliant but incredibly slow !!

[David Makin]

really nice stuff

Any chance to see that in 3D?

Thanks

3D ? Not so straightforward as in the interesting parts the patterns are continuous (though due to range limitations the whole pattern areas are bounded), you'd have to think very carefully about how to define a surface and more importantly how to efficiently find it !!

Edit: Of course converting to height-fields would be both possible and interesting

As to other folding types - will be investigating over the weekend

[David Makin]

I did try adding repeated folds/pleats prior to the rotation but repeating more than twice got very boring (basically the folding becomes too efficient reducing the variety) so the formula now simply has a user parameter to specify just one or two folds/pleats per iteration - will post an interesting result of using 2 instead of 1 this evening, now I have to get to work (am late because it's mum's birthday - she's 74) ttfn

[David Makin]

Here's "Bits'n'pieces" with two pleats per iteration applied prior to the rotation - without the extra pleat the result is akin to http://www.fractalforums.com/index.php?action=gallery;sa=view;id=9772



http://www.fractalforums.com/index.php?action=gallery;sa=view;id=9817

[David Makin]

The first released version of "Folded Patterns" is now uploaded to the UF formula database in mmf5.ucl - it really needs re-writing as a plug-in to make it more useful i.e. so it can be used for orbit trapping etc.
At the moment as it's an old-style colouring it's only useful for those main formulas that will work with the colourings that work for mt.ufm:pixel and similar.
Here's an example UPR (there are 2 more on the UF list for those who are members):

Code:

Fractal1 {
fractal:
  title="Fractal1" width=928 height=696 layers=1
  credits="Dave Makin;1/9/2012
layer:
  caption="Background" opacity=100 method=multipass
mapping:
  center=6.752249521/1.374375889 magn=0.2305399
formula:
  maxiter=1 percheck=off filename="mt.ufm" entry="mt-pixel"
  p_inside=no
inside:
  transfer=none
outside:
  density=0.9 transfer=linear filename="mmf5.ucl"
  entry="FoldedPatterns" p_p_version=1.0 p_p_scale=6/6 p_p_original=no
  p_p_seed=45/89 p_p_intseed=43 p_p_sym=yes p_p_detail=2
  p_p_folding=Square p_p_fader=0.5 p_p_fade=0.7 p_p_fade2=0.7
  p_p_twofolds=yes p_p_xscale=4 p_p_yscale=4 p_p_rfader=0.5
  p_p_rfade=0.5 p_p_rfade2=0.5 p_p_tworfolds=no p_p_rscale=2
  p_p_angle=9.345 p_p_reprot=2.2 p_p_universe=no p_p_self=0
gradient:
  smooth=yes rotation=1 index=0 color=16777215 index=106 color=43775
  index=156 color=13170 index=190 color=512 index=241 color=589830
  index=280 color=10007413
opacity:
  smooth=no index=0 opacity=255
}

Another:

Code:

Fractal2 {
fractal:
  title="Fractal2" width=928 height=696 layers=1
  credits="Dave Makin;1/9/2012;D J Makin;12/20/2011;Dave Makin;10/5/20\
  11;David Makin;6/15/2008;Frederik Slijkerman;7/23/2002"
layer:
  caption="Background" opacity=100 method=multipass
mapping:
  center=-4.736343266/0.6376322065 magn=0.4970953 angle=90
formula:
  maxiter=1 percheck=off filename="mt.ufm" entry="mt-pixel"
  p_inside=no
inside:
  transfer=none
outside:
  density=1.37 transfer=linear filename="mmf5.ucl"
  entry="FoldedPatterns" p_p_version=1.0 p_p_scale=6/6 p_p_original=no
  p_p_seed=45/89 p_p_intseed=43 p_p_sym=yes p_p_detail=2
  p_p_folding=Both p_p_fader=0.5 p_p_fade=0.7 p_p_fade2=0.7
  p_p_twofolds=yes p_p_xscale=2 p_p_yscale=2 p_p_rfader=0.5
  p_p_rfade=0.9 p_p_rfade2=0.5 p_p_tworfolds=yes p_p_rscale=2
  p_p_angle=9.345 p_p_reprot=2.2 p_p_universe=no p_p_self=0
gradient:
  smooth=yes rotation=1 index=0 color=16777215 index=106 color=43775
  index=188 color=19826 index=222 color=0 index=241 color=589830
  index=321 color=14087359
opacity:
  smooth=no index=0 opacity=255
}

[kram1032]

that image looks a lot better than your previous attempt, at least to my eye.

3D could possibly use different special material settings like continuous IoR, simple transparency, using maximum/minimum or equal values to define smooth implicit surfaces, varying volume materials...
Lots of different variants how this could be displayed in 3D. Some maybe more interesting, others simpler...

Heh, you could try some experiments like defining a cut-out surface of the Mbrot by cutting it with an implicit surface created by this process...

[David Makin]

that image looks a lot better than your previous attempt, at least to my eye.

3D could possibly use different special material settings like continuous IoR, simple transparency, using maximum/minimum or equal values to define smooth implicit surfaces, varying volume materials...
Lots of different variants how this could be displayed in 3D. Some maybe more interesting, others simpler...

Heh, you could try some experiments like defining a cut-out surface of the Mbrot by cutting it with an implicit surface created by this process...

Hmmm - but I don't think there's an easy distance estimation so you'd be stuck with essentially brute-force rendering, not exactly optimum !
Better to use the formula for non-random textures I think

[kram1032]

Wouldn't the distance estimation just be what ever technique you currently use as colour gradient but set a certain value of that, maybe with a delta to reduce possible artifacts, to a single value?
I'd guess to colour this stuff, you map the values from 0 to 1? So if you say "blah" = .5, you should get the values half way in between?

Or are you just operating on a gradient that you then transform by means of this fractal?
In THAT case, you could try to use an image as transformation target...
Or in the 3D case, some kind of voxel-structure, like, for instance, the classic mbox or mbulb or what ever variation.

[David Makin]

But there is no escape-time here, the entire thing is convergent so standard DE won't work - plus the values (say 0 to 1) are multiply wrapped resulting (in 3D terms) in a forest of usually similar sized disconnected objects (if you specify some range as "solid") - far less interesting than the Mandelbox for instance.
I guess it my be workable as a convergent bailout in iteration/distance estimation terms though I don't see how given that every fold is completely random.

In short I think the results are best used as stand-alones or as textures (of whatever kind).

[kram1032]

I see, so it will mostly be useful for 2D...

Hmm, did you try different kinds of randomness?
Like for instance, what about the next fold is selected in a brownian motion style way, where the new fold coordinates are chosen by only slightly offsetting the previous ones, both location and rotation...

Or what about randomly applying a couple of fixed patterns, rather than a totally random process?

[David Makin]

I see, so it will mostly be useful for 2D...

Hmm, did you try different kinds of randomness?
Like for instance, what about the next fold is selected in a brownian motion style way, where the new fold coordinates are chosen by only slightly offsetting the previous ones, both location and rotation...

Or what about randomly applying a couple of fixed patterns, rather than a totally random process?

Am planning on trying all those and more - but haven't done a line of code in the last 24 hours due to feeling like I've been hit by a bus - yesterday my nose was running like a tap, today it's almost dried up but I still feel rotten and spent most of the day just watching TV (or at least TV over the net) as I'm still having trouble concentrating on anything.....

[kram1032]

Oh, I've only seen that now!

I hope, enough time has passed to assume correctly, that at least the worst part of that is over.
Despite that, even if late:
Get well soon!

[David Makin]

Am much better but (as some may have noticed) I've been spending more time playing with my camera recently...http://makinmagic.deviantart.com/

I will be adding more to both the folding/pattern formula and the image tiling formula shortly - including an alternative version of the tiling formula that will do the same thing but essentially with live generated layers rather than loaded images.....oh - and a simplified alternative that may actually be superior (at least in terms of creating say surface textures for use in 3D or porting the code to do the same in shaders i.e. surface detail with texture-source-less tiled textures).