Hello,

since some people were wondering how I made some of my images, I decided to write a short tutorial on how to use the coupling loops formula in phs.ufm which I used several times over the last months.

When you first open it, this is what it looks like. The loopy stuff is located in the valleys of the main set and also the minibrots. As a rule of thumb, the higher c is, the stronger the perturbations. If you are looking for loops in small minibrots, you will have to pick very small values for c. Its also depends on Exponent 2. Play around with the values to get an idea. They explorer tool is great to find good values by zooming in or out until the changes become noticable but not too extreme.

61fd01391588e.png

Here, I changed the Coupling Shift from 50 to 350 (this will cause fewer perturbations and generate more parallel bands within the spirals). Then I zoomed into the valley between the main cardioid and the period 3 bulb (the one sitting right on top). You can clearly see the effect of the perturbations here.
61fd013a1a8f5.png
Make sure to turn off Periodicity Checking before activating the switching mode, or you will get a lot of false inside pixels. Using the switching mode in this area gave me this:
61fd0356c87d0.png

I zoomed into one of the spirals and increased the max iteration count from 15k to 125k):
61fd013a1c80c.png

One very simple thing you can do is reducing the color density greatly to stretch the gradient over the entire image, turn of Repeat Gradient, and modify it to your liking. Here's a very simple example:
61fd013a1c88e.png

Now you have all the option you have for any other shape, just be aware that these images can get quite costly to render because the iteration counts can get extremely high.
Parameters for last image:

Fractal3 {
fractal:
  title="Fractal3" width=694 height=545 layers=1
  credits="Phillip;2/4/2022"
layer:
  caption="Background" opacity=100
mapping:
  center=0.1027243919/-0.4305174228 magn=8.2482413
formula:
  maxiter=125000 percheck=off filename="phs.ufm"
  entry="coupling_loops_julia" p_dkmax=350 p_test=mod p_bailout=4.0
  p_c=0./0.1 p_exp1=2/0 p_exp2=1/0
  p_seed=-0.12040661310711/0.64956330496033
inside:
  transfer=none
outside:
  density=0.001947951 transfer=linear repeat=no
gradient:
  smooth=yes rotation=58 index=0 color=16777215 index=64 color=2756096
  index=137 color=13331232 index=226 color=16777197 index=320
  color=43775
opacity:
  smooth=no index=0 opacity=255
}

Have fun playing with this! smile

Hello, since some people were wondering how I made some of my images, I decided to write a short tutorial on how to use the coupling loops formula in phs.ufm which I used several times over the last months. When you first open it, this is what it looks like. The loopy stuff is located in the valleys of the main set and also the minibrots. As a rule of thumb, the higher **c** is, the stronger the perturbations. If you are looking for loops in small minibrots, you will have to pick very small values for **c**. Its also depends on **Exponent 2**. Play around with the values to get an idea. They explorer tool is great to find good values by zooming in or out until the changes become noticable but not too extreme. ![61fd01391588e.png](serve/attachment&path=61fd01391588e.png) Here, I changed the **Coupling Shift from 50 to 350** (this will cause fewer perturbations and generate more parallel bands within the spirals). Then I zoomed into the valley between the main cardioid and the period 3 bulb (the one sitting right on top). You can clearly see the effect of the perturbations here. ![61fd013a1a8f5.png](serve/attachment&path=61fd013a1a8f5.png) Make sure to turn off Periodicity Checking before activating the switching mode, or you will get a lot of false inside pixels. Using the switching mode in this area gave me this: ![61fd0356c87d0.png](serve/attachment&path=61fd0356c87d0.png) I zoomed into one of the spirals and increased the max iteration count from 15k to 125k): ![61fd013a1c80c.png](serve/attachment&path=61fd013a1c80c.png) One very simple thing you can do is reducing the color density greatly to stretch the gradient over the entire image, turn of Repeat Gradient, and modify it to your liking. Here's a very simple example: ![61fd013a1c88e.png](serve/attachment&path=61fd013a1c88e.png) Now you have all the option you have for any other shape, just be aware that these images can get quite costly to render because the iteration counts can get extremely high. Parameters for last image: ```` Fractal3 { fractal: title="Fractal3" width=694 height=545 layers=1 credits="Phillip;2/4/2022" layer: caption="Background" opacity=100 mapping: center=0.1027243919/-0.4305174228 magn=8.2482413 formula: maxiter=125000 percheck=off filename="phs.ufm" entry="coupling_loops_julia" p_dkmax=350 p_test=mod p_bailout=4.0 p_c=0./0.1 p_exp1=2/0 p_exp2=1/0 p_seed=-0.12040661310711/0.64956330496033 inside: transfer=none outside: density=0.001947951 transfer=linear repeat=no gradient: smooth=yes rotation=58 index=0 color=16777215 index=64 color=2756096 index=137 color=13331232 index=226 color=16777197 index=320 color=43775 opacity: smooth=no index=0 opacity=255 } ```` Have fun playing with this! :)
 
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Here's an image using Coupling Loops. Note the appearance of depth, especially if you view it full size.
alt="61fd4168c08df.jpg">
CouplingLoops+Quadrant {
::VbA0Pin2de1SPKOOQ47Ix/hocdFBbTeQmR+wO9ubrdUPrmVzjrITih4pdizmYaa4X/W2Jw0Q
ipbNcKUPdV1XVu8mGWmmJf30JeeahWyp+3p2VLFVb9eQpqb9+Nv/dHLvhVp992Ly1F0lIkXB
XstQTjhPlsD8mWKxYisGeuQ3S9/oo07Dyd83TmHOngIk3/5ChUKqPTw3DMpgJFsWwZ0D82pT
smyeWyY1ahqi6/ghkHItqmlJ0HoYwllcdhKnWuTqF1s2WPNc+arZN8KdnlKZ11gZ7sFQl3Qn
tIAlSQRxLjmjDiiSTiXEFF5Vy2WRRBokF44FwvpT2oaATzsKXyeWY0242aeTWBP7RqazGvNC
JviVCJsvoZV5sm8gdbK99An1cg6/Zxzcp/0JiqWROvL/aOkbAbVpq4Tno2pHyCS8cWjXrSKy
poX4kfIXHsLTe2+fXstir1civR/6VPB1ATCjgRR4IgQLUL4Vry0NmMCQw8FaOEFraY5idtQM
nmE1pdbBrmTjMMrV7hzh5LImekinOZrRewt2TabpSBYgKlXjSzs1oZYinoKn/MFTi9yUSFku
ijTwkFnZkgtViOehphECKunHhkcWpww0IS6JGLX2zA1TZBO5nm5MRwLdUIQ1snWS0AazOJGC
y9dgprioO5Qnhagu3ATivATOKkDFQSwIS0y0UMUXmPDFsINcxiUcUSKg+6we4lIoXYL07NDH
mEEnk4ACSiQuRh1FtWAoRjeMSWfn8KppTe1P2BNb+mC7jgJ7q2aermWqyhPXzESATSDDQdgi
MTXRYcEmMH+IaZcUMQl/cNmSs4I4TCFPvX8WOPnCRImgCRxx4FYUCG4GEDFVozCFmGjMtX/a
tEj1vlJfZ4ePvi3IyuvHuenpYDRffDSW/fvTCDM67nkrf3Hf4Dr+DRLYyM+t0I4pVb7sf3og
BcP9/Owwo63fwepkDErrz3ODboNOmfkecWtZ0yAedIoRd9GQrjebui6fRhBvFDtzProXZlv9
1LTbfSxXDzR+WLv5r2iFgZ9do5lpP3CpPZobL2OwnvRRH7USJu1ASWPNIXZZYyXu0ih6ntOC
L8NyoBMbH0osWjulirxw4CXaScppevKHQ7mpdDQenxlfSlPmuVQgMgo1aX2NZ2XgMKQwI8rj
E6l6UXJclGGhTdL55b+wYS44yAT44uCLrAnutsbutj2Prk5nmtPSu3KwNaEt8/PI9Q9hrPGT
isRynfRUWL5E3y/6p0s3eON7qkKszUoDhuVW9MaiYkYIWiQxuyQkri/7ENZSuTAF5thoIvdI
F5KMlb50Hg1m6OfOkoubx4xZ+mRdkgXB1RCauljKAKHpE3Rr+Wa3jodwVUtys2wfbvV3tRg9
KdM+gEkrg1VZgPckCaVl8VMpEab+dp0fIfNDigRrTFq9lsqDjfXrRNHAxe9Ijcm3br6VqxUr
evG2aKaYcaerC12pc9dL3P+9wrdNCPz6e/vzaE29v9WMSC5RR9K2TbdcKP+yR9DvBRUxk0/x
uR2IRo99BDhSnWfE/nkRP2N8MRt988avnId5pXNEd9DAwJp9USSxpxY7zX6ZtM5SWnonu8Xa
v//HsxuDLB==
}

Here's an image using Coupling Loops. Note the appearance of depth, especially if you view it full size. ![61fd4168c08df.jpg](serve/attachment&path=61fd4168c08df.jpg) CouplingLoops+Quadrant { ::VbA0Pin2de1SPKOOQ47Ix/hocdFBbTeQmR+wO9ubrdUPrmVzjrITih4pdizmYaa4X/W2Jw0Q ipbNcKUPdV1XVu8mGWmmJf30JeeahWyp+3p2VLFVb9eQpqb9+Nv/dHLvhVp992Ly1F0lIkXB XstQTjhPlsD8mWKxYisGeuQ3S9/oo07Dyd83TmHOngIk3/5ChUKqPTw3DMpgJFsWwZ0D82pT smyeWyY1ahqi6/ghkHItqmlJ0HoYwllcdhKnWuTqF1s2WPNc+arZN8KdnlKZ11gZ7sFQl3Qn tIAlSQRxLjmjDiiSTiXEFF5Vy2WRRBokF44FwvpT2oaATzsKXyeWY0242aeTWBP7RqazGvNC JviVCJsvoZV5sm8gdbK99An1cg6/Zxzcp/0JiqWROvL/aOkbAbVpq4Tno2pHyCS8cWjXrSKy poX4kfIXHsLTe2+fXstir1civR/6VPB1ATCjgRR4IgQLUL4Vry0NmMCQw8FaOEFraY5idtQM nmE1pdbBrmTjMMrV7hzh5LImekinOZrRewt2TabpSBYgKlXjSzs1oZYinoKn/MFTi9yUSFku ijTwkFnZkgtViOehphECKunHhkcWpww0IS6JGLX2zA1TZBO5nm5MRwLdUIQ1snWS0AazOJGC y9dgprioO5Qnhagu3ATivATOKkDFQSwIS0y0UMUXmPDFsINcxiUcUSKg+6we4lIoXYL07NDH mEEnk4ACSiQuRh1FtWAoRjeMSWfn8KppTe1P2BNb+mC7jgJ7q2aermWqyhPXzESATSDDQdgi MTXRYcEmMH+IaZcUMQl/cNmSs4I4TCFPvX8WOPnCRImgCRxx4FYUCG4GEDFVozCFmGjMtX/a tEj1vlJfZ4ePvi3IyuvHuenpYDRffDSW/fvTCDM67nkrf3Hf4Dr+DRLYyM+t0I4pVb7sf3og BcP9/Owwo63fwepkDErrz3ODboNOmfkecWtZ0yAedIoRd9GQrjebui6fRhBvFDtzProXZlv9 1LTbfSxXDzR+WLv5r2iFgZ9do5lpP3CpPZobL2OwnvRRH7USJu1ASWPNIXZZYyXu0ih6ntOC L8NyoBMbH0osWjulirxw4CXaScppevKHQ7mpdDQenxlfSlPmuVQgMgo1aX2NZ2XgMKQwI8rj E6l6UXJclGGhTdL55b+wYS44yAT44uCLrAnutsbutj2Prk5nmtPSu3KwNaEt8/PI9Q9hrPGT isRynfRUWL5E3y/6p0s3eON7qkKszUoDhuVW9MaiYkYIWiQxuyQkri/7ENZSuTAF5thoIvdI F5KMlb50Hg1m6OfOkoubx4xZ+mRdkgXB1RCauljKAKHpE3Rr+Wa3jodwVUtys2wfbvV3tRg9 KdM+gEkrg1VZgPckCaVl8VMpEab+dp0fIfNDigRrTFq9lsqDjfXrRNHAxe9Ijcm3br6VqxUr evG2aKaYcaerC12pc9dL3P+9wrdNCPz6e/vzaE29v9WMSC5RR9K2TbdcKP+yR9DvBRUxk0/x uR2IRo99BDhSnWfE/nkRP2N8MRt988avnId5pXNEd9DAwJp9USSxpxY7zX6ZtM5SWnonu8Xa v//HsxuDLB== }
 
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Here's something I cooked up after playing around a bit with this formula:

61fecb8fca4aa.jpg

Layers {
layer:
  caption="Layer 3" opacity=100
mapping:
  center=0.23288062843/-0.25487980326 magn=64.232405 angle=-35.7539
formula:
  maxiter=125000 percheck=off filename="phs.ufm"
  entry="coupling_loops_julia" p_dkmax=350
  p_test="imga/real + abs re(z) > 0" p_bailout=4.0
  p_c=0.0367047/0.0323002 p_exp1=2/0 p_exp2=1/0
  p_seed=-0.119941461/0.649627024
inside:
  transfer=none
outside:
  density=0.1052035 transfer=sqr
gradient:
  smooth=yes rotation=128 index=67 color=16777215 index=130 color=184
  index=201 color=13528348 index=301 color=0 index=366 color=1290495
opacity:
  smooth=no index=0 opacity=255
}
Here's something I cooked up after playing around a bit with this formula: ![61fecb8fca4aa.jpg](serve/attachment&path=61fecb8fca4aa.jpg) ```` Layers { layer: caption="Layer 3" opacity=100 mapping: center=0.23288062843/-0.25487980326 magn=64.232405 angle=-35.7539 formula: maxiter=125000 percheck=off filename="phs.ufm" entry="coupling_loops_julia" p_dkmax=350 p_test="imga/real + abs re(z) > 0" p_bailout=4.0 p_c=0.0367047/0.0323002 p_exp1=2/0 p_exp2=1/0 p_seed=-0.119941461/0.649627024 inside: transfer=none outside: density=0.1052035 transfer=sqr gradient: smooth=yes rotation=128 index=67 color=16777215 index=130 color=184 index=201 color=13528348 index=301 color=0 index=366 color=1290495 opacity: smooth=no index=0 opacity=255 } ````

Chris Martin
Gallery: Velvet--Glove.deviantart.com

Currently using UF6.04 on Windows 11 Professional 64-bit

 
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I cannot paste this nor use it as .upr, what exactly is this paste? smile

//edit: never mind, figured it out, it's a layer

I cannot paste this nor use it as .upr, what exactly is this paste? :) //edit: never mind, figured it out, it's a layer
edited Feb 6 at 11:31 am
 
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I cannot paste this nor use it as .upr, what exactly is this paste? smile

//edit: never mind, figured it out, it's a layer

Ack! Sorry about that, Phillip, I don't know how that happened I don't normally copy/paste layers! My bad. Glad you spotted it anyway and found the solution.

>I cannot paste this nor use it as .upr, what exactly is this paste? :) >//edit: never mind, figured it out, it's a layer Ack! Sorry about that, Phillip, I don't know how that happened I don't normally copy/paste layers! My bad. Glad you spotted it anyway and found the solution.

Chris Martin
Gallery: Velvet--Glove.deviantart.com

Currently using UF6.04 on Windows 11 Professional 64-bit

 
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For those who wonder what Velvet--Glove used: it's an old bailout test that I was working on and then just kind of forgot about. It doesn't do at all what it says, it actually just checks for the real part of z and if it's greater than zero, it bails out. I will tweak it to use @bailout instead, I will also correct a bug to keep the parameter settings when using the switching mode. I changed a name and forgot to update the switch part. smile

Does anyone know if I break existing fractals if I change the name of a bailout test? My gut feeling is that it uses integers to save what is used so renaming them should be fine, but I'm not sure smile

For those who wonder what Velvet--Glove used: it's an old bailout test that I was working on and then just kind of forgot about. It doesn't do at all what it says, it actually just checks for the real part of _z_ and if it's greater than zero, it bails out. I will tweak it to use _@bailout_ instead, I will also correct a bug to keep the parameter settings when using the switching mode. I changed a name and forgot to update the switch part. :) Does anyone know if I break existing fractals if I change the name of a bailout test? My gut feeling is that it uses integers to save what is used so renaming them should be fine, but I'm not sure :S
 
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