Does Ultra Fractal offer any of the lambda fractal planes, as described in this link? I am aware of the inverse fractal mapping but was wondering if any of these others are possible as well?

https://mathcs.clarku.edu/~djoyce/julia/altplane.html

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Does Ultra Fractal offer any of the lambda fractal planes, as described in this link? I am aware of the inverse fractal mapping but was wondering if any of these others are possible as well? https://mathcs.clarku.edu/~djoyce/julia/altplane.html ![5e2f03addbb14.png](serve/attachment&path=5e2f03addbb14.png)
 
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For the "lambda-plane", use the Lambda (Mandelbrot) formula in standard.ufm.

The others shown on that link are inversions on either lambda or the classic Mandelbrot. Add the Inverse mapping from standard.uxf, and set Center (Re) to the value to subtract.

For the "lambda-plane", use the Lambda (Mandelbrot) formula in standard.ufm. The others shown on that link are inversions on either lambda or the classic Mandelbrot. Add the Inverse mapping from standard.uxf, and set Center (Re) to the value to subtract.
 
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Thanks Rick, but I was hoping not to be limited to using only the Lambda Mandelbrot formula. What if I wish to put other fractal formulas such as Phoenix, Barnsley or Magnet in the various Lambda planes?

Thanks Rick, but I was hoping not to be limited to using only the Lambda Mandelbrot formula. What if I wish to put other fractal formulas such as Phoenix, Barnsley or Magnet in the various Lambda planes?
 
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I don't understand his use of the word "plane". All of the "planes" he describes are sets in the complex plane, represented graphically by two dimensional figures where x is the real axis and y is the complex axis. The "μ-plane" is the Mandelbrot set. The "lambda-plane" is the lambda fractal (the Julia version is known as the logistic map; the Julia Seed parameter is often represented with the Greek letter lambda (λ)). I suppose he would call the set obtained using the Phoenix (Mandelbrot) formula the "phoenix plane". I've never seen that terminology before, and don't know what it would mean to "put Phoenix in the Lambda plane".

I don't understand his use of the word "plane". All of the "planes" he describes are sets in the complex plane, represented graphically by two dimensional figures where x is the real axis and y is the complex axis. The "μ-plane" is the Mandelbrot set. The "lambda-plane" is the lambda fractal (the Julia version is known as the logistic map; the Julia Seed parameter is often represented with the Greek letter lambda (λ)). I suppose he would call the set obtained using the Phoenix (Mandelbrot) formula the "phoenix plane". I've never seen that terminology before, and don't know what it would mean to "put Phoenix in the Lambda plane".
 
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In addition to UF I also enjoy using another fractal program called XaoS fractal zoomer and it offers the six different fractal planes. I don't understand the math behind it, I'm just trying to mimic these options as closely as I can. It's no big deal, there is certainly enough to keep me busy with the inversion mapping.

I greatly appreciate your time and effort, Rick. I am including a few snips of info here for your general knowledge, thanks again.

5e3320cc88b86.png

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In addition to UF I also enjoy using another fractal program called XaoS fractal zoomer and it offers the six different fractal planes. I don't understand the math behind it, I'm just trying to mimic these options as closely as I can. It's no big deal, there is certainly enough to keep me busy with the inversion mapping. I greatly appreciate your time and effort, Rick. I am including a few snips of info here for your general knowledge, thanks again. ![5e3320cc88b86.png](serve/attachment&path=5e3320cc88b86.png) ![5e33213c9210d.png](serve/attachment&path=5e33213c9210d.png)
 
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I've never seen this terminology before, but it looks like what XaoS calls a "plane" is what UF calls a "mapping" or "transformation". The "mu plane" is normal mode, no mapping. The "1/mu plane" is done in UF with the Inverse mapping. To get the "lambda plane", we need a lambda mapping in UF. I found one in the public formulas! In the Mapping tab, choose "Plug-In Transformation" from standard.uxf. Then for its Transformation, go to thm.ulb and choose "THMLambdaMapping". To get something like the lambda plane image shown in the first post, use Mandelbrot as the formula and set the THMLambdaMapping parameter factor(Re) to 2. For the 1/lambda-plane, also change fn(z2) to recip. I don't see a way to get the 1/(lambda-1) plane; you'd probably need to write a new transformation.

I've never seen this terminology before, but it looks like what XaoS calls a "plane" is what UF calls a "mapping" or "transformation". The "mu plane" is normal mode, no mapping. The "1/mu plane" is done in UF with the Inverse mapping. To get the "lambda plane", we need a lambda mapping in UF. I found one in the public formulas! In the Mapping tab, choose "Plug-In Transformation" from standard.uxf. Then for its Transformation, go to thm.ulb and choose "THMLambdaMapping". To get something like the lambda plane image shown in the first post, use Mandelbrot as the formula and set the THMLambdaMapping parameter factor(Re) to 2. For the 1/lambda-plane, also change fn(z2) to recip. I don't see a way to get the 1/(lambda-1) plane; you'd probably need to write a new transformation.
 
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Rick, thanks for digging around on this, you've gone above and beyond. I've learned some cool stuff about transforms I didn't know before. I appreciate your time.

Rick, thanks for digging around on this, you've gone above and beyond. I've learned some cool stuff about transforms I didn't know before. I appreciate your time.
 
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