### (Question) Triangle Inequality Average Algorithm

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#### mikoval

• Fractal Friend
• Posts: 10

#### Triangle Inequality Average Algorithm

« on: May 24, 2018, 11:52:53 PM »
I have been struggling to understand the triangle inequality average algorithm, as well as simply getting some code working that produces reasonable results.

My code is based off the following paper:
http://jussiharkonen.com/files/on_fractal_coloring_techniques%28lo-res%29.pdf

I have created a shadertoy to show my existing code:

I have tried to follow as closely to the paper as I can however the results shown in the book:
https://imgur.com/a/boN3wSI

look nothing like mine at all.

It would be greatly appreciated if someone could give me some feedback. I have spent a bit of time trying to understand where I could be going wrong but am at a loss.

• Posts: 64

#### Re: Triangle Inequality Average Algorithm

« Reply #1 on: May 25, 2018, 04:27:33 PM »
I had to convert my code, here is a sample code, but be warned I have not tested it after the conversion.
I also included the complex.java code.

Code: [Select]
static double sum, sum2 = 0; static double mc = 0; public static double escapedValue(int n, Complex z, double bail, Complex p) { double temp = p.norm_squared(); double temp2 = z.norm_squared(); temp += 0.000000001; temp = Math.log(temp); double f = 1 - (Math.log(bail * bail) - temp) / (Math.log(temp2) - temp); if(n < 2) return f; sum = sum / n; sum2 = sum2 / (n - 1); return sum + (sum2 - sum) * f; } //n : iteration public static Complex iteratedFunction(Complex z, Complex c, int n) { Complex temp = z.square(); Complex temp2 = temp.plus(c); if(n == 0) { mc = c.norm(); } sum2 = sum; if(n != 0) { double mp = temp.norm(); double m = Math.abs(mp - mc); double M = mp + mc; sum += (temp2.norm() - m) / (M - m); } return temp2; } public static double iterate(Complex c) { Complex z = new Complex(); Complex p = new Complex(); //previous value int maxIter = 300; double bailout = 16; for(int i = 0; i < maxIter; i++) { if(z.norm() >= bailout) { return escapedValue(i, z, bailout, p); // used the returned value to select a color from a palette } p.assign(z); z = iteratedFunction(z, c, i); } return maxIter; }

• Fractal Furball
• Posts: 248

#### Re: Triangle Inequality Average Algorithm

« Reply #2 on: May 25, 2018, 04:42:32 PM »

• 3f
• Posts: 1518

#### Re: Triangle Inequality Average Algorithm

« Reply #3 on: May 26, 2018, 02:30:41 AM »
from Fragmentarium examples...

#### mikoval

• Fractal Friend
• Posts: 10

#### Re: Triangle Inequality Average Algorithm

« Reply #4 on: May 26, 2018, 07:16:59 AM »
Wow that you so much for the reply guys! and that fractal picture is absolutely gorgeous... wow. I actually went through your code and changed mine @superheal, however it didn't actually change the image that I was getting. Your code is nearly identical to mine. Maybe the problem is in my coloring algorithm... Can you possibly share a sample coloring algorithm that you are using with the result of the escapevalue function? I will spend a little more time going through the code though since I may have some silly mistake somewhere.

#### mikoval

• Fractal Friend
• Posts: 10

#### Re: Triangle Inequality Average Algorithm

« Reply #5 on: May 26, 2018, 07:18:05 AM »
Oh, I just noticed the fragment shader code for that image! Going to spend some time looking at it!

• Posts: 64

#### Re: Triangle Inequality Average Algorithm

« Reply #6 on: May 26, 2018, 11:34:34 AM »
Here is the complete code.

• Posts: 64

#### Re: Triangle Inequality Average Algorithm

« Reply #7 on: May 31, 2018, 12:01:46 AM »
I implemented the .frag code also, here is a sample image:

#### kosalos

• Fractal Friar
• Posts: 118

#### Re: Triangle Inequality Average Algorithm

« Reply #8 on: June 01, 2018, 01:14:44 AM »
I have posted a rendition for the iPad: https://github.com/Kosalos/BurningChicken

#### mikoval

• Fractal Friend
• Posts: 10

#### Re: Triangle Inequality Average Algorithm

« Reply #9 on: June 26, 2018, 08:44:25 AM »
Thank you so much for the responses guys. I spent a bit of time playing with the equations and learned a lot. Everything was really helpful. I tried making a fractal zoom using the curvature average in the end, but ran into problems with the zoom. Basically the value that you get as the result of the average sum converges slowly, so after zooming in a bit the pattern gets very small. I have been trying to find an equation to scale the values but haven't been able to find anything. Does anyone know anything about where to look? I have tried looking around but haven't seen much.

• Posts: 183

#### Re: Triangle Inequality Average Algorithm

« Reply #10 on: August 05, 2018, 02:36:30 PM »
You can spread the pattern by using values from iterations older than the penultimate one.
UF example, you can try with smoothing parameter disabled and/or turn off the "older iteration" option (implemented in "Trap Select"), with smoothing disabled the colour rate will need increasing:
Code: [Select]
TIAolderSmoothed {fractal:  title="TIAolderSmoothed" width=1272 height=954 layers=1 gamma=2.5  credits="David Makin;8/5/2018" antialiasing=yeslayer:  caption="Background" opacity=100mapping:  center=0.32860675362165/0.4852981212579 magn=11745.815formula:  maxiter=100 filename="Standard.ufm" entry="Mandelbrot" p_start=0/0  p_power=2/0 p_bailout=65536inside:  transfer=noneoutside:  density=2 transfer=linear filename="mmf5.ucl"  entry="GenericGradientColoringRenderFalse"  p_coloringClass="mmfnew.ulb:MMF_SmoothOrbitTraps"  p_coloringClass.v_generic=100 p_coloringClass.v_coloring=100  p_coloringClass.v_gradientcoloring=100  p_coloringClass.v_mmfsmoothorbittraps=1.0  p_coloringClass.smoothing=Divergent p_coloringClass.bailout=65536  p_coloringClass.dauto=yes p_coloringClass.power=2/0  p_coloringClass.fudge=1 p_coloringClass.smallbail=0.00001  p_coloringClass.cauto=yes p_coloringClass.cpower=2/0  p_coloringClass.fudgec=1 p_coloringClass.cfixed=no  p_coloringClass.cfixedval=1/0 p_coloringClass.processlast=yes  p_coloringClass.f_trapselect="dmj5.ulb:DMJ_TrapSelect"  p_coloringClass.f_trapselect.v_generic=100  p_coloringClass.f_trapselect.v_generator=100  p_coloringClass.f_trapselect.v_dmj_trapselect=100  p_coloringClass.f_trapselect.p_trapalliterations="some iterations"  p_coloringClass.f_trapselect.p_trapstart=0  p_coloringClass.f_trapselect.p_trapiter=1  p_coloringClass.f_trapselect.p_trapskip=3  p_coloringClass.f_trapselect.p_traploop=1E20  p_coloringClass.p_trapselectthreshold=0.5  p_coloringClass.f_traptransform="common.ulb:TrapTransform"  p_coloringClass.f_traptransform.v_generic=100  p_coloringClass.f_traptransform.v_transform=100  p_coloringClass.f_traptransform.v_usertransform=100  p_coloringClass.f_traptransform.v_traptransform=100  p_coloringClass.f_traptransform.p_trapcenter=0/0  p_coloringClass.f_traptransform.p_trapcentermoves=no  p_coloringClass.f_traptransform.p_trapdrift=0/0  p_coloringClass.f_traptransform.p_trapscale=1  p_coloringClass.f_traptransform.p_traprotation=0  p_coloringClass.f_traptransform.p_traprotationstep=0  p_coloringClass.f_traptransform.p_trapskew=0  p_coloringClass.f_traptransform.p_trapskewstep=0  p_coloringClass.f_traptransform.p_trapaspect=1  p_coloringClass.f_trapshape="mmfnew.ulb:MMF_TrapShapeTriangleInequal\  ity" p_coloringClass.f_trapshape.v_generic=100  p_coloringClass.f_trapshape.v_trapshape=101  p_coloringClass.f_trapshape.p_usepixel=yes  p_coloringClass.f_trapshape.p_tcentre=1/0  p_coloringClass.f_fixzold=yes  p_coloringClass.f_traptransfer="common.ulb:TrapTransfer"  p_coloringClass.f_traptransfer.v_generic=100  p_coloringClass.f_traptransfer.v_transfer=100  p_coloringClass.f_traptransfer.v_traptransfer=100  p_coloringClass.f_traptransfer.p_preadd1=0  p_coloringClass.f_traptransfer.p_prescale=1  p_coloringClass.f_traptransfer.p_preadd2=0  p_coloringClass.f_traptransfer.p_function=linear  p_coloringClass.f_traptransfer.p_postadd1=0  p_coloringClass.f_traptransfer.p_postscale=1  p_coloringClass.f_traptransfer.p_postadd2=0  p_coloringClass.f_traptransfer.p_abs=no  p_coloringClass.f_trapmode="mmfnew.ulb:MMF_TrapModeSmoothAverage"  p_coloringClass.f_trapmode.v_generic=100  p_coloringClass.f_trapmode.v_trapmode=100  p_coloringClass.f_trapmode.v_trapmodewiththreshold=100  p_coloringClass.f_trapmode.v_mmf_trapmodesmoothwiththreshold=100  p_coloringClass.p_threshold=1 p_coloringClass.p_usesolid=no  p_coloringClass.f_traptexture="dmj5.ulb:DMJ_TrapShapeFlat"  p_coloringClass.f_traptexture.v_generic=100  p_coloringClass.f_traptexture.v_trapshape=101  p_coloringClass.f_traptexture.v_dmj_trapshapeflat=100  p_coloringClass.p_texturepositiononly=no  p_coloringClass.p_textureposttransform=no  p_coloringClass.p_texturestrength=1  p_coloringClass.f_trapcoloring="mmfnew.ulb:MMF_TrapColoring"  p_coloringClass.f_trapcoloring.v_generic=100  p_coloringClass.f_trapcoloring.v_trapcoloring=100  p_coloringClass.f_trapcoloring.v_mmf_trapcoloring=100  p_coloringClass.f_trapcoloring.colourby=Distance  p_coloringClass.f_trapcoloring.f_image="mmfnew.ulb:MMF_ImageImport"  p_coloringClass.f_trapcoloring.f_image.v_generic=100  p_coloringClass.f_trapcoloring.f_image.v_imagewrapper=100  p_coloringClass.f_trapcoloring.f_image.v_imageimport=101  p_coloringClass.f_trapcoloring.f_image.p_importedimage=""  p_coloringClass.f_trapcoloring.f_image.p_maintainaspect=yes  p_coloringClass.f_trapcoloring.f_image.p_transform="common.ulb:NullT\  ransform"  p_coloringClass.f_trapcoloring.f_image.p_transform.v_generic=100  p_coloringClass.f_trapcoloring.f_image.p_transform.v_transform=100  p_coloringClass.f_trapcoloring.f_image.p_transform.v_usertransform=1\  00  p_coloringClass.f_trapcoloring.f_image.p_transform.v_nulltransform=1\  00 p_coloringClass.f_trapcoloring.f_image.p_tile=yes  p_coloringClass.f_trapcoloring.f_image.p_iterate=no  p_coloringClass.f_trapcoloring.f_image.p_transform1="common.ulb:Null\  Transform"  p_coloringClass.f_trapcoloring.f_image.p_transform1.v_generic=100  p_coloringClass.f_trapcoloring.f_image.p_transform1.v_transform=100  p_coloringClass.f_trapcoloring.f_image.p_transform1.v_usertransform=\  100  p_coloringClass.f_trapcoloring.f_image.p_transform1.v_nulltransform=\  100 p_coloringClass.f_trapcoloring.f_image.p_retile=no  p_coloringClass.f_trapcoloring.f_image.p_mirror=no  p_coloringClass.f_trapcoloring.f_image.p_flip=no  p_coloringClass.f_trapcoloring.f_image.p_seamless=yes  p_coloringClass.f_trapcoloring.f_image.p_normalise=no  p_coloringClass.f_trapcoloring.f_image.p_grey24=no  p_coloringClass.f_trapcoloring.f_image.adjustlayer=no  p_coloringClass.f_trapcoloring.f_image.adjusttype="Colour Parameter"  p_coloringClass.f_trapcoloring.f_image.adjred=1  p_coloringClass.f_trapcoloring.f_image.adjgreen=1  p_coloringClass.f_trapcoloring.f_image.adjblue=1  p_coloringClass.f_trapcoloring.f_image.f_adjustcolour=4294967295  p_coloringClass.f_trapcoloring.f_image.f_adjust="mmfnew.ulb:MMF_Exte\  ndedColorMerge"  p_coloringClass.f_trapcoloring.f_image.f_adjust.v_generic=100  p_coloringClass.f_trapcoloring.f_image.f_adjust.v_colormerge=100  p_coloringClass.f_trapcoloring.f_image.f_adjust.v_defaultcolormerge=\  100  p_coloringClass.f_trapcoloring.f_image.f_adjust.v_mmfextendedcolorme\  rge=1.0  p_coloringClass.f_trapcoloring.f_image.f_adjust.p_modeselect="Origin\  al Merge Modes"  f_coloringClass.f_trapcoloring.f_image.f_adjust.f_mergemode=multiply  p_coloringClass.f_trapcoloring.f_image.f_adjust.clamp=no  p_coloringClass.f_trapcoloring.f_image.f_adjust.p_mmfmergemode=Exclu\  sion p_coloringClass.f_trapcoloring.f_image.f_adjust.qmin=2  p_coloringClass.f_trapcoloring.f_image.f_adjust.qmax=32  p_coloringClass.f_trapcoloring.f_image.f_adjust.mingamma=1  p_coloringClass.f_trapcoloring.f_image.f_adjust.maxgamma=2  p_coloringClass.f_trapcoloring.f_image.f_adjust.redlvl=0.299  p_coloringClass.f_trapcoloring.f_image.f_adjust.greenlvl=0.587  p_coloringClass.f_trapcoloring.f_image.f_adjust.bluelvl=0.114  p_coloringClass.f_trapcoloring.f_image.f_opacity=1  p_coloringClass.f_trapcoloring.f_image.f_adjustment="mmfnew.ulb:MMF_\  AdjustmentLayer"  p_coloringClass.f_trapcoloring.f_image.f_adjustment.v_generic=100  p_coloringClass.f_trapcoloring.f_image.f_adjustment.v_adjustmentlaye\  r=100  p_coloringClass.f_trapcoloring.f_image.f_adjustment.v_mmfadjustmentl\  ayer=1.0  p_coloringClass.f_trapcoloring.f_image.f_adjustment.adjusttype="Colo\  ur Parameter"  p_coloringClass.f_trapcoloring.f_image.f_adjustment.adjred=1  p_coloringClass.f_trapcoloring.f_image.f_adjustment.adjgreen=1  p_coloringClass.f_trapcoloring.f_image.f_adjustment.adjblue=1  p_coloringClass.f_trapcoloring.f_image.f_adjustment.f_adjustcolour=4\  294967295  p_coloringClass.f_trapcoloring.f_image.f_adjustment.f_adjust="mmfnew\  .ulb:MMF_ExtendedColorMerge"  p_coloringClass.f_trapcoloring.f_image.f_adjustment.f_adjust.v_gener\  ic=100  p_coloringClass.f_trapcoloring.f_image.f_adjustment.f_adjust.v_color\  merge=100  p_coloringClass.f_trapcoloring.f_image.f_adjustment.f_adjust.v_defau\  ltcolormerge=100  p_coloringClass.f_trapcoloring.f_image.f_adjustment.f_adjust.v_mmfex\  tendedcolormerge=1.0  p_coloringClass.f_trapcoloring.f_image.f_adjustment.f_adjust.p_modes\  elect="Original Merge Modes"  f_coloringClass.f_trapcoloring.f_image.f_adjustment.f_adjust.f_merge\  mode=multiply  p_coloringClass.f_trapcoloring.f_image.f_adjustment.f_adjust.clamp=n\  o  p_coloringClass.f_trapcoloring.f_image.f_adjustment.f_adjust.p_mmfme\  rgemode=Exclusion  p_coloringClass.f_trapcoloring.f_image.f_adjustment.f_adjust.qmin=2  p_coloringClass.f_trapcoloring.f_image.f_adjustment.f_adjust.qmax=32  p_coloringClass.f_trapcoloring.f_image.f_adjustment.f_adjust.mingamm\  a=1  p_coloringClass.f_trapcoloring.f_image.f_adjustment.f_adjust.maxgamm\  a=2  p_coloringClass.f_trapcoloring.f_image.f_adjustment.f_adjust.redlvl=\  0.299  p_coloringClass.f_trapcoloring.f_image.f_adjustment.f_adjust.greenlv\  l=0.587  p_coloringClass.f_trapcoloring.f_image.f_adjustment.f_adjust.bluelvl\  =0.114  p_coloringClass.f_trapcoloring.f_image.f_adjustment.f_opacity=1  p_coloringClass.f_trapcoloring.f_image.p_wrap=no  p_coloringClass.f_trapcoloring.f_image.p_usefbm=no  p_coloringClass.f_trapcoloring.f_image.p_fbm="mmfnew.ulb:MMF_AltfBm"  p_coloringClass.f_trapcoloring.f_image.p_fbm.v_generic=100  p_coloringClass.f_trapcoloring.f_image.p_fbm.v_mmfaltfbm=1.0  p_coloringClass.f_trapcoloring.f_image.p_fbm.mode="Div 16"  p_coloringClass.f_trapcoloring.f_image.p_fbm.seed=123456  p_coloringClass.f_trapcoloring.f_image.p_fbm.rs=1  p_coloringClass.f_trapcoloring.f_image.p_fbm.frac=0.7071  p_coloringClass.f_trapcoloring.f_image.p_fbm.mainamp=1  p_coloringClass.f_trapcoloring.f_image.p_fbm.average=Normal  p_coloringClass.f_trapcoloring.f_image.p_fbm.inter=Linear  p_coloringClass.f_trapcoloring.f_image.p_fbm.dice=1  p_coloringClass.f_trapcoloring.f_image.p_fbm.dummy=0  p_coloringClass.f_trapcoloring.f_image.p_fbm.morph=no  p_coloringClass.f_trapcoloring.f_image.p_fbm.exp=1  p_coloringClass.f_trapcoloring.f_image.p_fbm.gamma=no  p_coloringClass.f_trapcoloring.f_image.p_fbm.mid=0.5  p_coloringClass.f_trapcoloring.f_image.p_fbm.lowp=1.5  p_coloringClass.f_trapcoloring.f_image.p_fbm.highp=0.66666666667  p_coloringClass.f_trapcoloring.f_image.p_fbm.levels=8  p_coloringClass.f_trapcoloring.f_image.p_fbm.showmaps=no  p_coloringClass.f_trapcoloring.f_image.p_fbm.flag0=yes  p_coloringClass.f_trapcoloring.f_image.p_fbm.frac0=0.7071  p_coloringClass.f_trapcoloring.f_image.p_fbm.rs0=1  p_coloringClass.f_trapcoloring.f_image.p_fbm.amp0=1  p_coloringClass.f_trapcoloring.f_image.p_fbm.ang0=0  p_coloringClass.f_trapcoloring.f_image.p_fbm.flag1=yes  p_coloringClass.f_trapcoloring.f_image.p_fbm.frac1=0.7071  p_coloringClass.f_trapcoloring.f_image.p_fbm.rs1=1  p_coloringClass.f_trapcoloring.f_image.p_fbm.amp1=1  p_coloringClass.f_trapcoloring.f_image.p_fbm.ang1=22.5  p_coloringClass.f_trapcoloring.f_image.p_fbm.flag2=yes  p_coloringClass.f_trapcoloring.f_image.p_fbm.frac2=0.7071  p_coloringClass.f_trapcoloring.f_image.p_fbm.rs2=1  p_coloringClass.f_trapcoloring.f_image.p_fbm.amp2=1  p_coloringClass.f_trapcoloring.f_image.p_fbm.ang2=11.25  p_coloringClass.f_trapcoloring.f_image.p_fbm.flag3=yes  p_coloringClass.f_trapcoloring.f_image.p_fbm.frac3=0.7071  p_coloringClass.f_trapcoloring.f_image.p_fbm.rs3=1  p_coloringClass.f_trapcoloring.f_image.p_fbm.amp3=1  p_coloringClass.f_trapcoloring.f_image.p_fbm.ang3=33.75  p_coloringClass.f_trapcoloring.f_image.p_fbm.flag4=yes  p_coloringClass.f_trapcoloring.f_image.p_fbm.frac4=0.7071  p_coloringClass.f_trapcoloring.f_image.p_fbm.rs4=1  p_coloringClass.f_trapcoloring.f_image.p_fbm.amp4=1  p_coloringClass.f_trapcoloring.f_image.p_fbm.ang4=16.875  p_coloringClass.f_trapcoloring.f_image.p_fbm.flag5=yes  p_coloringClass.f_trapcoloring.f_image.p_fbm.frac5=0.7071  p_coloringClass.f_trapcoloring.f_image.p_fbm.rs5=1  p_coloringClass.f_trapcoloring.f_image.p_fbm.amp5=1  p_coloringClass.f_trapcoloring.f_image.p_fbm.ang5=39.375  p_coloringClass.f_trapcoloring.f_image.p_fbm.flag6=yes  p_coloringClass.f_trapcoloring.f_image.p_fbm.frac6=0.7071  p_coloringClass.f_trapcoloring.f_image.p_fbm.rs6=1  p_coloringClass.f_trapcoloring.f_image.p_fbm.amp6=1  p_coloringClass.f_trapcoloring.f_image.p_fbm.ang6=28.125  p_coloringClass.f_trapcoloring.f_image.p_fbm.flag7=yes  p_coloringClass.f_trapcoloring.f_image.p_fbm.frac7=0.7071  p_coloringClass.f_trapcoloring.f_image.p_fbm.rs7=1  p_coloringClass.f_trapcoloring.f_image.p_fbm.amp7=1  p_coloringClass.f_trapcoloring.f_image.p_fbm.ang7=5.625  p_coloringClass.f_trapcoloring.f_image.p_fbm.flag8=yes  p_coloringClass.f_trapcoloring.f_image.p_fbm.frac8=0.7071  p_coloringClass.f_trapcoloring.f_image.p_fbm.rs8=2  p_coloringClass.f_trapcoloring.f_image.p_fbm.amp8=0.5  p_coloringClass.f_trapcoloring.f_image.p_fbm.ang8=19.6875  p_coloringClass.f_trapcoloring.f_image.p_fbm.flag9=yes  p_coloringClass.f_trapcoloring.f_image.p_fbm.frac9=0.7071  p_coloringClass.f_trapcoloring.f_image.p_fbm.rs9=2  p_coloringClass.f_trapcoloring.f_image.p_fbm.amp9=0.5  p_coloringClass.f_trapcoloring.f_image.p_fbm.ang9=36.5625  p_coloringClass.f_trapcoloring.f_image.p_fbm.flag10=yes  p_coloringClass.f_trapcoloring.f_image.p_fbm.frac10=0.7071  p_coloringClass.f_trapcoloring.f_image.p_fbm.rs10=2  p_coloringClass.f_trapcoloring.f_image.p_fbm.amp10=0.5  p_coloringClass.f_trapcoloring.f_image.p_fbm.ang10=8.4375  p_coloringClass.f_trapcoloring.f_image.p_fbm.flag11=yes  p_coloringClass.f_trapcoloring.f_image.p_fbm.frac11=0.7071  p_coloringClass.f_trapcoloring.f_image.p_fbm.rs11=4  p_coloringClass.f_trapcoloring.f_image.p_fbm.amp11=0.25  p_coloringClass.f_trapcoloring.f_image.p_fbm.ang11=25.3125  p_coloringClass.f_trapcoloring.f_image.p_fbm.flag12=yes  p_coloringClass.f_trapcoloring.f_image.p_fbm.frac12=0.7071  p_coloringClass.f_trapcoloring.f_image.p_fbm.rs12=4  p_coloringClass.f_trapcoloring.f_image.p_fbm.amp12=0.25  p_coloringClass.f_trapcoloring.f_image.p_fbm.ang12=14.0625  p_coloringClass.f_trapcoloring.f_image.p_fbm.flag13=yes  p_coloringClass.f_trapcoloring.f_image.p_fbm.frac13=0.7071  p_coloringClass.f_trapcoloring.f_image.p_fbm.rs13=8  p_coloringClass.f_trapcoloring.f_image.p_fbm.amp13=0.125  p_coloringClass.f_trapcoloring.f_image.p_fbm.ang13=30.9375  p_coloringClass.f_trapcoloring.f_image.p_fbm.flag14=yes  p_coloringClass.f_trapcoloring.f_image.p_fbm.frac14=0.7071  p_coloringClass.f_trapcoloring.f_image.p_fbm.rs14=16  p_coloringClass.f_trapcoloring.f_image.p_fbm.amp14=0.0625  p_coloringClass.f_trapcoloring.f_image.p_fbm.ang14=2.8125  p_coloringClass.f_trapcoloring.f_image.p_fbm.flag15=yes  p_coloringClass.f_trapcoloring.f_image.p_fbm.frac15=0.7071  p_coloringClass.f_trapcoloring.f_image.p_fbm.rs15=32  p_coloringClass.f_trapcoloring.f_image.p_fbm.amp15=0.03125  p_coloringClass.f_trapcoloring.f_image.p_fbm.ang15=42.1875  p_coloringClass.f_trapcoloring.f_image.p_deflect=0  p_coloringClass.f_trapcoloring.f_image.p_twotile=no  p_coloringClass.f_trapcoloring.f_image.p_tileimage=""  p_coloringClass.f_trapcoloring.f_image.p_patternx=000  p_coloringClass.f_trapcoloring.f_image.p_patterny=0x0  p_coloringClass.f_trapcoloring.f_image.p_xgutter=0.5  p_coloringClass.f_trapcoloring.f_image.p_ygutter=0.5  p_coloringClass.f_trapcoloring.f_image.p_xoff=0  p_coloringClass.f_trapcoloring.f_image.p_yoff=0  p_coloringClass.f_trapcoloring.f_image.p_advanced=no  p_coloringClass.f_trapcoloring.f_image.p_rotate=yes  p_coloringClass.f_trapcoloring.f_image.p_random=yes  p_coloringClass.f_trapcoloring.f_image.p_rand=yes  p_coloringClass.f_trapcoloring.f_image.p_seedit=yes  p_coloringClass.f_trapcoloring.f_image.p_seed=10083  p_coloringClass.f_trapcoloring.f_image.p_gbasex=0.2  p_coloringClass.f_trapcoloring.f_image.p_gmaxx=0.8  p_coloringClass.f_trapcoloring.f_image.p_gbasey=0.2  p_coloringClass.f_trapcoloring.f_image.p_gmaxy=0.8  p_coloringClass.f_trapcoloring.f_image.p_xgutter00=0.5  p_coloringClass.f_trapcoloring.f_image.p_xgutter01=0.5  p_coloringClass.f_trapcoloring.f_image.p_xgutter10=0.5  p_coloringClass.f_trapcoloring.f_image.p_xgutter11=0.5  p_coloringClass.f_trapcoloring.f_image.p_ygutter00=0.5  p_coloringClass.f_trapcoloring.f_image.p_ygutter01=0.5  p_coloringClass.f_trapcoloring.f_image.p_ygutter10=0.5  p_coloringClass.f_trapcoloring.f_image.p_ygutter11=0.5  p_coloringClass.f_trapcoloring.f_image.p_xoff00=0  p_coloringClass.f_trapcoloring.f_image.p_xoff01=0  p_coloringClass.f_trapcoloring.f_image.p_xoff10=0  p_coloringClass.f_trapcoloring.f_image.p_xoff11=0  p_coloringClass.f_trapcoloring.f_image.p_yoff00=0  p_coloringClass.f_trapcoloring.f_image.p_yoff01=0  p_coloringClass.f_trapcoloring.f_image.p_yoff10=0  p_coloringClass.f_trapcoloring.f_image.p_yoff11=0  p_coloringClass.f_trapcoloring.f_image.p_SimplefBm=0  p_coloringClass.f_trapcoloring.f_image.p_scale=0.5  p_coloringClass.f_trapcoloring.f_image.p_fade=0.5  p_coloringClass.f_trapcoloring.usetrap="Original Z value"  p_coloringClass.f_trapcoloring.f_colortransfer="common.ulb:NullTrans\  fer" p_coloringClass.f_trapcoloring.f_colortransfer.v_generic=100  p_coloringClass.f_trapcoloring.f_colortransfer.v_transfer=100  p_coloringClass.f_trapcoloring.f_colortransfer.v_nulltransfer=100  p_coloringClass.f_trapcoloring.f_texturetransfer="common.ulb:NullTra\  nsfer"  p_coloringClass.f_trapcoloring.f_texturetransfer.v_generic=100  p_coloringClass.f_trapcoloring.f_texturetransfer.v_transfer=100  p_coloringClass.f_trapcoloring.f_texturetransfer.v_nulltransfer=100  p_coloringClass.f_trapcoloring.f_merge="mmfnew.ulb:MMF_GradientLayer\  " p_coloringClass.f_trapcoloring.f_merge.v_generic=100  p_coloringClass.f_trapcoloring.f_merge.v_layer=100  p_coloringClass.f_trapcoloring.f_merge.f_solid=4278190080  p_coloringClass.f_trapcoloring.f_merge.f_invertmerge=no  p_coloringClass.f_trapcoloring.f_merge.f_invertcompose=no  p_coloringClass.f_trapcoloring.f_merge.f_opacity=1  p_coloringClass.f_trapcoloring.f_merge.f_merge="mmfnew.ulb:MMF_Exten\  dedColorMerge"  p_coloringClass.f_trapcoloring.f_merge.f_merge.v_generic=100  p_coloringClass.f_trapcoloring.f_merge.f_merge.v_colormerge=100  p_coloringClass.f_trapcoloring.f_merge.f_merge.v_defaultcolormerge=1\  00  p_coloringClass.f_trapcoloring.f_merge.f_merge.v_mmfextendedcolormer\  ge=1.0  p_coloringClass.f_trapcoloring.f_merge.f_merge.p_modeselect="Origina\  l Merge Modes"  f_coloringClass.f_trapcoloring.f_merge.f_merge.f_mergemode=multiply  p_coloringClass.f_trapcoloring.f_merge.f_merge.clamp=no  p_coloringClass.f_trapcoloring.f_merge.f_merge.p_mmfmergemode=Exclus\  ion p_coloringClass.f_trapcoloring.f_merge.f_merge.qmin=2  p_coloringClass.f_trapcoloring.f_merge.f_merge.qmax=32  p_coloringClass.f_trapcoloring.f_merge.f_merge.mingamma=1  p_coloringClass.f_trapcoloring.f_merge.f_merge.maxgamma=2  p_coloringClass.f_trapcoloring.f_merge.f_merge.redlvl=0.299  p_coloringClass.f_trapcoloring.f_merge.f_merge.greenlvl=0.587  p_coloringClass.f_trapcoloring.f_merge.f_merge.bluelvl=0.114  p_coloringClass.f_trapcoloring.f_merge.v_gradientlayer=100  p_coloringClass.f_trapcoloring.f_merge.f_grad="Custom Gradient"  p_coloringClass.f_trapcoloring.f_merge.f_gradient="mmfnew.ulb:MMF_Gr\  adient"  p_coloringClass.f_trapcoloring.f_merge.f_gradient.v_generic=100  p_coloringClass.f_trapcoloring.f_merge.f_gradient.v_mmfgradientbase=\  100  p_coloringClass.f_trapcoloring.f_merge.f_gradient.v_mmfgradient=1.0  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_transfer="common\  .ulb:DefaultGradientTransfer"  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_transfer.v_gener\  ic=100  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_transfer.v_trans\  fer=100  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_transfer.v_defau\  ltgradienttransfer=101  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_transfer.p_xfer=\  Linear  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_transfer.p_zscal\  e=1.0  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_transfer.p_zscal\  e2=1.0  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_transfer.p_offse\  t=0.0 p_coloringClass.f_trapcoloring.f_merge.f_gradient.rept=yes  p_coloringClass.f_trapcoloring.f_merge.f_gradient.smooth=yes  p_coloringClass.f_trapcoloring.f_merge.f_gradient.showpalette=no  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours="mmfn\  ew.ulb:MMF_FourKeyColours"  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.v_gen\  eric=100  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.v_mmf\  keycolourbase=100  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.v_mmf\  fourkeycolours=100  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.numco\  ls=4  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.colou\  r0=4278190213  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.index\  0=0  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.colou\  r1=4294967295  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.index\  1=100  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.colou\  r2=4294948096  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.index\  2=200  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.colou\  r3=4288413696  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.index\  3=300  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.colou\  r4=4294967040  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.index\  4=50  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.colou\  r5=4278255615  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.index\  5=150  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.colou\  r6=4294902015  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.index\  6=250  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.colou\  r7=4294967295  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.index\  7=350  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.colou\  r8=4294934783  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.index\  8=75  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.colou\  r9=4286644223  p_coloringClass.f_trapcoloring.f_merge.f_gradient.f_keycolours.index\  9=325 p_coloringClass.f_trapcoloring.f_merge.adjustlayer=no  p_coloringClass.f_trapcoloring.f_merge.f_adjustment="mmfnew.ulb:MMF_\  AdjustmentLayer"  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.v_generic=100  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.v_adjustmentlaye\  r=100  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.v_mmfadjustmentl\  ayer=1.0  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.adjusttype="Colo\  ur Parameter"  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.adjred=1  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.adjgreen=1  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.adjblue=1  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.f_adjustcolour=4\  294967295  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.f_adjust="mmfnew\  .ulb:MMF_ExtendedColorMerge"  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.f_adjust.v_gener\  ic=100  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.f_adjust.v_color\  merge=100  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.f_adjust.v_defau\  ltcolormerge=100  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.f_adjust.v_mmfex\  tendedcolormerge=1.0  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.f_adjust.p_modes\  elect="Original Merge Modes"  f_coloringClass.f_trapcoloring.f_merge.f_adjustment.f_adjust.f_merge\  mode=multiply  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.f_adjust.clamp=n\  o  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.f_adjust.p_mmfme\  rgemode=Exclusion  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.f_adjust.qmin=2  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.f_adjust.qmax=32  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.f_adjust.mingamm\  a=1  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.f_adjust.maxgamm\  a=2  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.f_adjust.redlvl=\  0.299  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.f_adjust.greenlv\  l=0.587  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.f_adjust.bluelvl\  =0.114  p_coloringClass.f_trapcoloring.f_merge.f_adjustment.f_opacity=1  p_coloringClass.f_trapcoloring.f_merge.v_mmfgradientlayer=1.0  p_coloringClass.f_trapcoloring.adjustlayer=no  p_coloringClass.f_trapcoloring.adjusttype="Colour Parameter"  p_coloringClass.f_trapcoloring.adjred=1  p_coloringClass.f_trapcoloring.adjgreen=1  p_coloringClass.f_trapcoloring.adjblue=1  p_coloringClass.f_trapcoloring.f_adjustcolour=4294967295  p_coloringClass.f_trapcoloring.f_adjust="mmfnew.ulb:MMF_ExtendedColo\  rMerge" p_coloringClass.f_trapcoloring.f_adjust.v_generic=100  p_coloringClass.f_trapcoloring.f_adjust.v_colormerge=100  p_coloringClass.f_trapcoloring.f_adjust.v_defaultcolormerge=100  p_coloringClass.f_trapcoloring.f_adjust.v_mmfextendedcolormerge=1.0  p_coloringClass.f_trapcoloring.f_adjust.p_modeselect="Original Merg\  e Modes"  f_coloringClass.f_trapcoloring.f_adjust.f_mergemode=multiply  p_coloringClass.f_trapcoloring.f_adjust.clamp=no  p_coloringClass.f_trapcoloring.f_adjust.p_mmfmergemode=Exclusion  p_coloringClass.f_trapcoloring.f_adjust.qmin=2  p_coloringClass.f_trapcoloring.f_adjust.qmax=32  p_coloringClass.f_trapcoloring.f_adjust.mingamma=1  p_coloringClass.f_trapcoloring.f_adjust.maxgamma=2  p_coloringClass.f_trapcoloring.f_adjust.redlvl=0.299  p_coloringClass.f_trapcoloring.f_adjust.greenlvl=0.587  p_coloringClass.f_trapcoloring.f_adjust.bluelvl=0.114  p_coloringClass.f_trapcoloring.f_opacity=1  p_coloringClass.f_finaltransfer="mmfnew.ulb:MMF_TrapTransfer"  p_coloringClass.f_finaltransfer.v_generic=100  p_coloringClass.f_finaltransfer.v_transfer=100  p_coloringClass.f_finaltransfer.v_mmf_traptransfer=100  p_coloringClass.f_finaltransfer.p_offset0=0  p_coloringClass.f_finaltransfer.p_zscale0=1  p_coloringClass.f_finaltransfer.p_offset1=0  p_coloringClass.f_finaltransfer.p_forcepos=no  p_coloringClass.f_finaltransfer.p_xfer=Linear  p_coloringClass.f_finaltransfer.p_iatpower=2  p_coloringClass.f_finaltransfer.p_power=4  p_coloringClass.f_finaltransfer.p_offset2=0  p_coloringClass.f_finaltransfer.p_zscale1=1  p_coloringClass.f_finaltransfer.p_offset3=0  p_coloringClass.f_additer=yes  p_coloringClass.f_itertransfer="mmfnew.ulb:MMF_TrapTransfer"  p_coloringClass.f_itertransfer.v_generic=100  p_coloringClass.f_itertransfer.v_transfer=100  p_coloringClass.f_itertransfer.v_mmf_traptransfer=100  p_coloringClass.f_itertransfer.p_offset0=0  p_coloringClass.f_itertransfer.p_zscale0=1  p_coloringClass.f_itertransfer.p_offset1=0  p_coloringClass.f_itertransfer.p_forcepos=no  p_coloringClass.f_itertransfer.p_xfer=Linear  p_coloringClass.f_itertransfer.p_iatpower=2  p_coloringClass.f_itertransfer.p_power=4  p_coloringClass.f_itertransfer.p_offset2=0  p_coloringClass.f_itertransfer.p_zscale1=1  p_coloringClass.f_itertransfer.p_offset3=0gradient:  smooth=yes rotation=-138 index=120 color=145 index=180 color=46591  index=-181 color=8024433 index=-38 color=16121855opacity:  smooth=no index=0 opacity=255}
The meaning and purpose of life is to give life purpose and meaning.

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