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Author Topic: Is there anything novel left to do in M-like escape-time fractals in 2d?  (Read 26960 times)
Description: I think there may be. Your opinions are greatly desired.
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Dinkydau
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« Reply #315 on: May 07, 2013, 12:26:04 AM »

Looks really good
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simon.snake
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« Reply #316 on: May 07, 2013, 12:10:48 PM »

Thanks.
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simon.snake
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simon.fez SimonSideBurns
« Reply #317 on: May 12, 2013, 12:14:17 AM »

I've started writing a Fractal eXtreme plugin of the fractal I've written.  So far, it zooms up to 45 times, now got to complete it by writing the trickier bit...  Will continue this thread in the Fractal eXtreme plugin section of the forum (here).
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To anyone viewing my posts and finding missing/broken links to a website called www.needanother.co.uk, I still own the domain but recently cancelled my server (saving ú30/month) so even though the domain address exists, it points nowhere.  I hope to one day sort something out but for now - sorry!
element90
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« Reply #318 on: May 29, 2013, 05:13:05 PM »

Back in reply #272 of this thread I shared some pictures using Gnofract4d. I'm adding the formulae to version 4.0.0 of Saturn and Titan. Now that I've had more time to play with them I noticed some odd things about one of the formulae.

The formula

z = (c(z^3 - z^4) + 1)^5

where initial value of z is 0.75 and c is the location in complex plane.

Oddly, along the real axis the pictures exhibit the blocky nature of fractals that have been produced with insufficient precision at low levels of zoom, i.e at about -8.94 + 0i and a width of 0.03 I get this:



Closer to zero and the width that shows this problem gets significantly smaller at -8 + 0i it only gets blocky at a width of 1e-7.

Elsewhere in the fractal I get this:



Which Gnofract4d makes a mess of:



Zooming in further with Saturn I get:



The whole nature of the spiral unexpectedly changes its character.

Does anybody know what is going on? I haven't yet been able to see what an increase in precision will do to the unexpectedly blocky parts of the fractal as Saturn currently only increases precision automatically, there is no manual override (this feature will be added soon).
« Last Edit: May 26, 2014, 12:08:28 PM by element90, Reason: Replaced file links. » Logged

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Roquen
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« Reply #319 on: July 14, 2013, 02:02:25 PM »

It sounds like the operations are formed in a way leading which lead to catastrophic cancellation.  Example: x2-y2 is a numerically bad computation.  Sound familiar?
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element90
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« Reply #320 on: July 14, 2013, 02:36:08 PM »

Roquen: that looks like likely explanation.

Increasing precision solves the problem but the amount it is increased by is down to seeing what the image looks like for each increment. Saturn now allows precision to be set manually and allows increments of 16 bits.
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Roquen
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« Reply #321 on: July 14, 2013, 03:09:41 PM »

Well that's good news.  However increasing precision simply pushes back the problem.  Using GLSL as an example of a couple simple tricks:

Code:
// z*z
vec2 pow2(vec2 z)
{
  float x = (z.x + z.y)*(z.x - z.y);  // not (z.x*z.x - z.y*z.y) .. removes the catastrophic cancellation
  float y = z.x * z.y;
  return vec2(x, y+y);
}

vec2 pow3(vec2 z) { return cmul(pow2(z), z); }
vec2 pow4(vec2 z) { return pow2(pow2(z)); }
vec2 pow5(vec2 z) { return cmul(pow4(z), z); }
vec2 pow6(vec2 z) { return pow2(pow3(z)); }
// etc, etc.

and likewise pullout powers when possible: z3-z4 = z2(z-z2)
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element90
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« Reply #322 on: July 14, 2013, 05:52:13 PM »

The problem occurs with a formula that has complex parameters for complex powers so in C++ std::complex<T> std::pow(std::complex<T>, std::complex<T>) is used, so I have no means of removing the "catastrophic cancellation". All formulae in Saturn are built in, there is no facility for editing formula like there is in other programs such as UF.
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fracmonk
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« Reply #323 on: August 30, 2013, 10:54:18 PM »

In case anyone's curious, I'm still kickin', but I've been better.  Have been looking in without logging in.  Did some new stuff, related to the old stuff, nothing presentable yet.  I need the time and energy...hope you're all feeling vastly better than I am!

Later.
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Nahee_Enterprises
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« Reply #324 on: August 30, 2013, 11:29:15 PM »

    In case anyone's curious, I'm still kickin', but I've been better.   ..... 
    I need the time and energy... hope you're all feeling vastly better than I am!

Glad to see you are still hanging around.  Sounds like you are not doing all that well, so I hope you feel better soon, at least better than I have been.     smiley
 
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fracmonk
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« Reply #325 on: September 05, 2013, 11:41:51 PM »

Paul,

Thanx for your kindness.  Compassion seems scarce and unfashionable.  It's very good to hear from you again after all this time.  What's been on my mind lately is that from the most complex human organizations right down to the simplest microbes, we're just under attack all the time.  We just have to fight all the time to survive as long as we can while we can, and I guess that's the game.  My experience lately observes a kind of pathological competitiveness that forces us to do things in undesirable ways.  For me, chief among these what I see as a nightmare of electronic dependency that many embrace as the best thing since sliced bread, but I see it ending badly.  Involvement for me in that is minimal, and many might say that it's an age thing, what they may not get is that with age comes experience, which is undervalued.  I find things, as here, and must use an electronic venue to communicate them, but I'd rather there was another way.  I need *simpler* badly!  That you're still in the fight is extremely gratifying to me.  Be well.

Later.
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Nahee_Enterprises
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« Reply #326 on: September 06, 2013, 05:24:15 AM »

    What's been on my mind lately is that from the most complex human organizations right down to the simplest microbes,
    we're just under attack all the time.  We just have to fight all the time to survive as long as we can while we can, and
    I guess that's the game.     ......     That you're still in the fight is extremely gratifying to me.

Personally, I am just trying to hang on long enough to see the end of modern civilization (and most likely, mankind), which at the current rate of destruction should not be that far away.

    For me, chief among these what I see as a nightmare of electronic dependency that many embrace as the best thing
    since sliced bread, but I see it ending badly.    .....but I'd rather there was another way.  I need *simpler* badly!

Dependency on electricity is not a good thing, but at this point in history, it is where we are currently at.  The biggest problem is HOW we create most of that electricity.  We have nuclear plants melting down poisoning everything around them for decades, fossil fuels burning and polluting, dammed up water altering landscapes and restricting aquatic life, etc....
 
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Alef
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« Reply #327 on: September 07, 2013, 03:46:07 PM »

Quote
For me, chief among these what I see as a nightmare of electronic dependency that many embrace as the best thing since sliced bread, but I see it ending badly.
Funny to complain about this in fully computer forums.
Sliced bread is great thing. Well, I think we can survive another few nuclear accidents, there even are people living in Chernobil area. Sea level rise could be worst I think.

But doing population census in neigbourhood I noticed marked cultural shift among generations. Many senior russians as an education listed church community schools. But then it's paranoia and nationalism among youth. Less open, less willing or able to communicate, hiding some secrets. It's even with writing a  postcard vs. new facebook likes and SMS.
The same thing all around European countries. And no progress exept in smartphone market. + wild unnemployment rates amoung periphery european youth and cousy supermarket in place of factory which once produced this thing:



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fractal catalisator
fracmonk
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« Reply #328 on: September 09, 2013, 05:45:31 PM »

I was just trying to convey my extreme unease with being forced to use these vicious devices to communicate or be incompetent without them.  By vicious, I mean that they are designed in part to betray us.

I have no particular objections to electricity use; it would be better if such expanded awareness and knowledge, but most is not used that way.  Means of generation, as Paul suggested, often leaves much to be desired, as well.
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Alef
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« Reply #329 on: September 18, 2013, 06:17:24 PM »

fracmonk, here I rendered orbit plot of your even power multipowerbrot from somewhere of the star of this thread. z= sqr( ( sqr( z*z*c +1 )) -1 ) -1 Thread had become hudge;)

It needs just eyes.


Code:
a_b_multipowereven_slow {
; Depending on PC 'ill take long time to render.
fractal:
  title="a_b_multipowereven_slow" width=800 height=600 layers=1
  credits="Alef;9/18/2013;Asdam;6/26/2013"
layer:
  caption="Background" opacity=100 transparent=yes
mapping:
  center=-0.4592812905/0 magn=1.1378451
formula:
  maxiter=100 filename="Standard.ufm" entry="Pixel"
inside:
  transfer=none
outside:
  transfer=linear filename="em.ucl" entry="Brahmabrot"
  p_sampleDensity=15000 p_maxiter=550 p_seedinput=-8
  p_formula="Multipowerbrot Even" p_power=2 p_starpower=7
  p_stargeom=0.5 p_unitvector=-0.5 p_talisadd=1 p_quadfactor=2.5
  p_frequency=1 p_spin=1 p_centralorbit=0.25/0 p_settype=Mset
  p_julia=-0.4/0.25 p_srcWidth=6 p_srcHeight=5
  p_switchRGB="Switch Green and Blue" p_ambient=0.15
  p_postfn="10- Sigmoid" p_palette="Mixed Harmonic" p_equalisation=no
  p_sigmoidlight=20 p_lightR=0.38 p_scalarR=0.7 p_lightG=0.98
  p_scalarG=1.6 p_lightB=0.15 p_scalarB=0.3
gradient:
  smooth=yes index=0 color=4605510 index=55 color=8323072 index=101
  color=16711680 index=141 color=16744319 index=211 color=16777215
  index=261 color=8388607 index=311 color=65535 index=361 color=32639
opacity:
  smooth=yes index=50 opacity=255 index=100 opacity=255 index=200
  opacity=255 index=302 opacity=255 index=376 opacity=255
}


* multipowerbrot_even.jpg (128.42 KB, 800x600 - viewed 59 times.)
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fractal catalisator
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