Does anyone know how to write a formula for this fractal?

I've seen it called a teardrop or mandeldrop fractal, but after much experimentation have been unable to recreate it.

There may already be a formula for this in the database, but I couldn't find one.

Does anyone know how to write a formula for this fractal? http://www.relativitybook.com/CoolStuff/erkfractals/mandeldrop_small.gif I&#039;ve seen it called a teardrop or mandeldrop fractal, but after much experimentation have been unable to recreate it. There may already be a formula for this in the database, but I couldn&#039;t find one.
edited Dec 7 '15 at 1:29 pm

0

The Mandelbrot at a glance

Inverse

The Mandelbrot doesn't exist outside a circle of radius 2 on the complex plane, this gives scope for turning it inside out by mapping z0 to 1/z0. The result, center at (1.4,0), is as follows.

.
.
.

Mandelscott: The Inverse of Fun

You may recall that the Mandelbrot set is generated by iterating the equation z = z^2 + c, where z = c at the start. We take a point on the complex plane, square it and add the original point. We take that answer, square it and add the original point. Then we take the new answer, square it and add the original point. We do this many times (which is why it can only done by computers) for every point on the screen. If the point trends toward infinity, we give it a color; if it sticks around near the starting point, we leave it black.

When I finally realized I needed to invert both z and c, I got the Mandeldrop set.

[The Mandelbrot at a glance](http://paulbourke.net/fractals/mandelbrot/) Inverse The Mandelbrot doesn&#039;t exist outside a circle of radius 2 on the complex plane, this gives scope for turning it inside out by mapping z0 to 1/z0. The result, center at (1.4,0), is as follows. http://paulbourke.net/fractals/mandelbrot/inverse.gif . . . [Mandelscott: The Inverse of Fun](http://mandelscott.blogspot.com/2011/11/inverse-of-fun.html) &gt; You may recall that the Mandelbrot set is generated by iterating the equation z = z^2 + c, where z = c at the start. We take a point on the complex plane, square it and add the original point. We take that answer, square it and add the original point. Then we take the new answer, square it and add the original point. We do this many times (which is why it can only done by computers) for every point on the screen. If the point trends toward infinity, we give it a color; if it sticks around near the starting point, we leave it black. &gt; When I finally realized I needed to invert both z and c, I got the Mandeldrop set.

0

Closest I could find after a quick search.

`Extrapolation1InverseInMmfUfm.upr {fractal:  title="Extrapolation 1 Inverse in mmf ufm.upr" width=480 height=720  layers=1 credits="K M F;12/7/2015"layer:  caption="Layer 3" opacity=100 method=multipassmapping:  center=-3.9598223385/-10.036702265 magn=0.15829525 angle=153.0271formula:  maxiter=2048 filename="mmf.ufm" entry="MMFz-Extra1I" p_z0=0/-4  p_z2=1/0 p_power=3.0/0 p_test=mod p_bailout=65536.0  p_smallbail=disabled p_bailout1=1E-5 p_ang=0.0 p_xy=1/4 p_m=1/0  p_n=0/1 p_sigma=no p_selfrot=Disabled p_invert=no p_centre=0/0  p_radius=1.0 f_Fn1=ident f_Fn2=identinside:  transfer=cube filename="Standard.ucl" entry="Default"outside:  density=0.1 transfer=log repeat=no filename="Standard.ucl"  entry="Default"gradient:  smooth=no rotation=2 index=401 color=16777215 index=2 color=16777215  index=26 color=0 index=51 color=16777215 index=76 color=0 index=101  color=16777215 index=126 color=5 index=151 color=16777215 index=176  color=0 index=201 color=16777215 index=226 color=0 index=251  color=16777215 index=276 color=0 index=301 color=16777215 index=326  color=0 index=351 color=16777215 index=376 color=0opacity:  smooth=no index=0 opacity=255}`

Closest I could find after a quick search. ![5665af9e54fad.png](serve/attachment&amp;path=5665af9e54fad.png) Extrapolation1InverseInMmfUfm.upr { fractal: title=&quot;Extrapolation 1 Inverse in mmf ufm.upr&quot; width=480 height=720 layers=1 credits=&quot;K M F;12/7/2015&quot; layer: caption=&quot;Layer 3&quot; opacity=100 method=multipass mapping: center=-3.9598223385/-10.036702265 magn=0.15829525 angle=153.0271 formula: maxiter=2048 filename=&quot;mmf.ufm&quot; entry=&quot;MMFz-Extra1I&quot; p_z0=0/-4 p_z2=1/0 p_power=3.0/0 p_test=mod p_bailout=65536.0 p_smallbail=disabled p_bailout1=1E-5 p_ang=0.0 p_xy=1/4 p_m=1/0 p_n=0/1 p_sigma=no p_selfrot=Disabled p_invert=no p_centre=0/0 p_radius=1.0 f_Fn1=ident f_Fn2=ident inside: transfer=cube filename=&quot;Standard.ucl&quot; entry=&quot;Default&quot; outside: density=0.1 transfer=log repeat=no filename=&quot;Standard.ucl&quot; entry=&quot;Default&quot; gradient: smooth=no rotation=2 index=401 color=16777215 index=2 color=16777215 index=26 color=0 index=51 color=16777215 index=76 color=0 index=101 color=16777215 index=126 color=5 index=151 color=16777215 index=176 color=0 index=201 color=16777215 index=226 color=0 index=251 color=16777215 index=276 color=0 index=301 color=16777215 index=326 color=0 index=351 color=16777215 index=376 color=0 opacity: smooth=no index=0 opacity=255 }

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Thanks Encrypted. The parameters you gave produce exactly what I was looking for. So I looked at the text file for the formula used for these parameters, which is Extrapolation #1 (Inverse) in mmf.ufm. Unfortunately this formula is too advanced for me to understand. It's possible a formula for this fractal is beyond my current capabilities, but I will keep trying....

Thanks Encrypted. The parameters you gave produce exactly what I was looking for. So I looked at the text file for the formula used for these parameters, which is Extrapolation #1 (Inverse) in mmf.ufm. Unfortunately this formula is too advanced for me to understand. It&#039;s possible a formula for this fractal is beyond my current capabilities, but I will keep trying....

0

Open the standard default and then you need to use the Mapping Tab and Add a Transformation which is called Inverse.
If you look in the manual you can find a description of this. Look for Transformations.

Inverse

The Inverse transformation turns a fractal inside out. The original center of the fractal is put infinitely far away, and points that were far away end up near the center. Inverse is available as a transformation in Standard.uxf and as a transformation plug-in in Standard.ulb.

Peter

Open the standard default and then you need to use the Mapping Tab and Add a Transformation which is called Inverse. If you look in the manual you can find a description of this. Look for Transformations. Inverse The Inverse transformation turns a fractal inside out. The original center of the fractal is put infinitely far away, and points that were far away end up near the center. Inverse is available as a transformation in Standard.uxf and as a transformation plug-in in Standard.ulb. Peter

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Here are the parameters for you to paste.

`InvertedMandelbrotColouredForForum {fractal:  title="Inverted Mandelbrot Coloured for Forum" width=900 height=720  layers=1 resolution=200 credits="Peter Shepheard;12/7/2015"layer:  caption="Background" opacity=100 method=multipassmapping:  center=1.004849/0 magn=0.4 angle=270 transforms=1transform:  filename="Standard.uxf" entry="Inverse" p_radius=1.0 p_center=0/0  p_usescreen=noformula:  maxiter=100 percheck=off filename="Standard.ufm" entry="Mandelbrot"  p_start=0/0 p_power=2/0 p_bailout=1e20inside:  transfer=noneoutside:  density=2 transfer=linear solid=4286722382 filename="Standard.ucl"  entry="Basic" p_type=Iterationgradient:  comments="Default Ultra Fractal gradient." smooth=yes rotation=-2  index=123 color=368977 index=170 color=65278 index=298 color=156  index=-3 color=16384000opacity:  smooth=no index=0 opacity=255}`

Here are the parameters for you to paste. InvertedMandelbrotColouredForForum { fractal: title=&quot;Inverted Mandelbrot Coloured for Forum&quot; width=900 height=720 layers=1 resolution=200 credits=&quot;Peter Shepheard;12/7/2015&quot; layer: caption=&quot;Background&quot; opacity=100 method=multipass mapping: center=1.004849/0 magn=0.4 angle=270 transforms=1 transform: filename=&quot;Standard.uxf&quot; entry=&quot;Inverse&quot; p_radius=1.0 p_center=0/0 p_usescreen=no formula: maxiter=100 percheck=off filename=&quot;Standard.ufm&quot; entry=&quot;Mandelbrot&quot; p_start=0/0 p_power=2/0 p_bailout=1e20 inside: transfer=none outside: density=2 transfer=linear solid=4286722382 filename=&quot;Standard.ucl&quot; entry=&quot;Basic&quot; p_type=Iteration gradient: comments=&quot;Default Ultra Fractal gradient.&quot; smooth=yes rotation=-2 index=123 color=368977 index=170 color=65278 index=298 color=156 index=-3 color=16384000 opacity: smooth=no index=0 opacity=255 }
edited Dec 8 '15 at 11:13 am

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Thanks, Peter. Yes, that also gives the teardrop fractal. I will experiment further with that transformation.

Thanks both Peter and Encrypted for your help. After puzzling over this for a few days, your answers have spurred me on and I've now written a formula which approximates what I was looking for. It can be found as f462 in om.ufm, and looks like this:

Here's params if anyone wants to play:

`mandeldrop {fractal:  title="mandeldrop" width=1024 height=768 layers=1  credits="Otto;12/7/2015"layer:  caption="Background" opacity=100mapping:  center=0.01/0.12 magn=6formula:  maxiter=250 filename="om.ufm" entry="f462" f_fn=ident p_var=0/1.8inside:  transfer=noneoutside:  transfer=lineargradient:  smooth=yes index=0 color=8716288 index=100 color=16121855 index=200  color=46591 index=300 color=156opacity:  smooth=no index=0 opacity=255}`

Thanks, Peter. Yes, that also gives the teardrop fractal. I will experiment further with that transformation. Thanks both Peter and Encrypted for your help. After puzzling over this for a few days, your answers have spurred me on and I&#039;ve now written a formula which approximates what I was looking for. It can be found as f462 in om.ufm, and looks like this: ![5665d8eb97cb9.png](serve/attachment&amp;path=5665d8eb97cb9.png) Here&#039;s params if anyone wants to play: mandeldrop { fractal: title=&quot;mandeldrop&quot; width=1024 height=768 layers=1 credits=&quot;Otto;12/7/2015&quot; layer: caption=&quot;Background&quot; opacity=100 mapping: center=0.01/0.12 magn=6 formula: maxiter=250 filename=&quot;om.ufm&quot; entry=&quot;f462&quot; f_fn=ident p_var=0/1.8 inside: transfer=none outside: transfer=linear gradient: smooth=yes index=0 color=8716288 index=100 color=16121855 index=200 color=46591 index=300 color=156 opacity: smooth=no index=0 opacity=255 }
edited Dec 12 '15 at 10:06 am

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SO I took you up on your advice and played with your formula - this is what I come up with:

`mandeldropOnTheSun {::YXI8sgn2tf1SvxtNQ47Gw/HE2ep9wuLf/oB8QTbQRKSQBiTRPGwViaNj1rqH2ezv+MkUaXvp  bQbAK6JbAbLODnZIn5bmPpyeb+ot6Hv+qssR/Ylzsq22U4qK6b7yabyGv1lNM1sK7Bfx4tGB  Cldrzv/2RjUoyqsHc9DGaw8e3Qb10ovtxQFos8eXhfcA8n/OX2up87eBmsFz3SQY+L+9xx2w  aZc5qrvK6p4xI32FdyqXazvbff7UTxqs2Obuf8ghhzqd97d1tFOT9U1ovr6w1XVb768N7T27  aGd9G0GtWxoSmWr5bRb4MpGLgfkZ129NGC76rKb7BfYjmVbf0HsDD3QbxHnGGNHcDZl+KXjt  GyLFd1bmKrXlB+v/gZ1vt+9H6c/0qgxdfYw5KgYSkItKEOmUopsZFEDeDjKIEIBsBR0SWQTX  7DQ8IbRJPsz6ranGNYiCW9HDuXP+L+5TRyNtdmV3A/PjsCkUAKtN5Oza0GEO4FfzgvwFvNFO  45Q+Kbs32MUCBqy34s9P5CdDYehtvYzUe1xb17792m9Vu5r18ZcD68D41XBP8/Xw23bL8gNx  oNU32CIxQapvd0GxKYtOzDw2HNMtMLvtqFKkMEkmTSB9RoRUhSiFElaWFRTWMQIhCDdxTUGd  RBWTkCZsONrDiXSHXyD+eGf+0DYT78mRHRvEO/iI93EElhPBzDgwT48h2yxqQPXK/2Z7hcRI  B8VA+IGGJQKGXKoaugpoKKmCgSCRrwcElDaUcC0RowCeC9DtEiNUKYGR+KMeuUCNIDGy1Xdc  VMSnKrO3Dbmes8YFFWvuo+jrv5QdtDkEAqx7wqXC5ks3677bhBDr+SPCjO8Fw1WrIKmUqeSI  GKHPLEv7138uvDfP0IhDefor9O3ghngQBgy0AkD4wiTJE4uHAVHxLpl+m7d9jQh6bcSQ75DC  KZCohs8DlNGojoZMdSu3GjMWAYHpG67VIYCgiqvYfq6UrT+0OXPggmzJUlEgoYGTfem/txx0  7grU2bDzB/T79usfOgJB8wZdZpdG30DwmOvZbbIRkjtGGRJkQ9XLCCIBBaAIB/GFQjCYMJhg  YJPkziWRR05Ba3W27+LshTTp3c8uoeCTpxx6BJIQjhJ+c+cBLnGlRhrJiijeNJQLQSEL6mcQ  gURQAkVFdTe80qZhczibiy0aoFGHPws84BGLJSeM44igb0AyXTTnmgAlUIYQHxibiyIMCNdl  yZRBIiQgT3BsLGcoBDxj7gEFAAXK01t4GXM9x1Q+kEdTcTACAJV0lUFxwxMZKX9Y0rhgoWSv  HC+gApcqM6jPF2iiA3IWIRNEchBWjTuYI1nd7QV2OvdYhXCqzGWcDVRDm3dF0xH4rWkTMa2R  FEQz8pIqkCTuYnUTB1iFdMDW9Ulsgykt1fxJCEV6XI0gnG91QnLWmWV7bAlQbdy4gkQjYoNM  hnO2h8mE5yskEQmu5LpRRoFDBmyuKburOM2ceSgbI3CvtTMcXiLj834yaLLHcR/u0ZS1MBQY  w4n3ZeRquf1ONMAsdvGGJt31vKO+ZcEeDCYASVbb/3/pfYukFJW2dI8mTNbrdW4P2HzSElg6  GYUFYTY/h0kNPwYudOvVGVXO1kb6d5+u4Ixmi2a/nczJ+06hggwbOgkkAzAFASzV829zvMD+  rz8uwslIBhhEQ/6CjqYhbkCgZopdhDmjOxBD4eqgKEL8poFSYhkjliLSoeGj/aGeJe8nyvuE  Mk8cW3FmbsSchtTIsLIdNGpusXWLU/jk6X61XDgnvFOctQzhxlK4VH1MO7EFOTD6UapiLCvg  0MBOGUDgeB5ZC8nJwfmA/ZC8nJw/PjA/43q+1+Q1XRQ/L+S11AIbhEJ84l+k01E8TpKFYCUh  ORKd0Kmgrxn4qW2PX8N99ofG9rOZyD==}`

SO I took you up on your advice and played with your formula - this is what I come up with: mandeldropOnTheSun { ::YXI8sgn2tf1SvxtNQ47Gw/HE2ep9wuLf/oB8QTbQRKSQBiTRPGwViaNj1rqH2ezv+MkUaXvp bQbAK6JbAbLODnZIn5bmPpyeb+ot6Hv+qssR/Ylzsq22U4qK6b7yabyGv1lNM1sK7Bfx4tGB Cldrzv/2RjUoyqsHc9DGaw8e3Qb10ovtxQFos8eXhfcA8n/OX2up87eBmsFz3SQY+L+9xx2w aZc5qrvK6p4xI32FdyqXazvbff7UTxqs2Obuf8ghhzqd97d1tFOT9U1ovr6w1XVb768N7T27 aGd9G0GtWxoSmWr5bRb4MpGLgfkZ129NGC76rKb7BfYjmVbf0HsDD3QbxHnGGNHcDZl+KXjt GyLFd1bmKrXlB+v/gZ1vt+9H6c/0qgxdfYw5KgYSkItKEOmUopsZFEDeDjKIEIBsBR0SWQTX 7DQ8IbRJPsz6ranGNYiCW9HDuXP+L+5TRyNtdmV3A/PjsCkUAKtN5Oza0GEO4FfzgvwFvNFO 45Q+Kbs32MUCBqy34s9P5CdDYehtvYzUe1xb17792m9Vu5r18ZcD68D41XBP8/Xw23bL8gNx oNU32CIxQapvd0GxKYtOzDw2HNMtMLvtqFKkMEkmTSB9RoRUhSiFElaWFRTWMQIhCDdxTUGd RBWTkCZsONrDiXSHXyD+eGf+0DYT78mRHRvEO/iI93EElhPBzDgwT48h2yxqQPXK/2Z7hcRI B8VA+IGGJQKGXKoaugpoKKmCgSCRrwcElDaUcC0RowCeC9DtEiNUKYGR+KMeuUCNIDGy1Xdc VMSnKrO3Dbmes8YFFWvuo+jrv5QdtDkEAqx7wqXC5ks3677bhBDr+SPCjO8Fw1WrIKmUqeSI GKHPLEv7138uvDfP0IhDefor9O3ghngQBgy0AkD4wiTJE4uHAVHxLpl+m7d9jQh6bcSQ75DC KZCohs8DlNGojoZMdSu3GjMWAYHpG67VIYCgiqvYfq6UrT+0OXPggmzJUlEgoYGTfem/txx0 7grU2bDzB/T79usfOgJB8wZdZpdG30DwmOvZbbIRkjtGGRJkQ9XLCCIBBaAIB/GFQjCYMJhg YJPkziWRR05Ba3W27+LshTTp3c8uoeCTpxx6BJIQjhJ+c+cBLnGlRhrJiijeNJQLQSEL6mcQ gURQAkVFdTe80qZhczibiy0aoFGHPws84BGLJSeM44igb0AyXTTnmgAlUIYQHxibiyIMCNdl yZRBIiQgT3BsLGcoBDxj7gEFAAXK01t4GXM9x1Q+kEdTcTACAJV0lUFxwxMZKX9Y0rhgoWSv HC+gApcqM6jPF2iiA3IWIRNEchBWjTuYI1nd7QV2OvdYhXCqzGWcDVRDm3dF0xH4rWkTMa2R FEQz8pIqkCTuYnUTB1iFdMDW9Ulsgykt1fxJCEV6XI0gnG91QnLWmWV7bAlQbdy4gkQjYoNM hnO2h8mE5yskEQmu5LpRRoFDBmyuKburOM2ceSgbI3CvtTMcXiLj834yaLLHcR/u0ZS1MBQY w4n3ZeRquf1ONMAsdvGGJt31vKO+ZcEeDCYASVbb/3/pfYukFJW2dI8mTNbrdW4P2HzSElg6 GYUFYTY/h0kNPwYudOvVGVXO1kb6d5+u4Ixmi2a/nczJ+06hggwbOgkkAzAFASzV829zvMD+ rz8uwslIBhhEQ/6CjqYhbkCgZopdhDmjOxBD4eqgKEL8poFSYhkjliLSoeGj/aGeJe8nyvuE Mk8cW3FmbsSchtTIsLIdNGpusXWLU/jk6X61XDgnvFOctQzhxlK4VH1MO7EFOTD6UapiLCvg 0MBOGUDgeB5ZC8nJwfmA/ZC8nJw/PjA/43q+1+Q1XRQ/L+S11AIbhEJ84l+k01E8TpKFYCUh ORKd0Kmgrxn4qW2PX8N99ofG9rOZyD== } ![5670a055286a9.png](serve/attachment&amp;path=5670a055286a9.png)
edited Dec 15 '15 at 11:20 pm

0

Looks good, and I like the 'page curl' effect...

Looks good, and I like the &#039;page curl&#039; effect...

0

That formula was a rather distorted version. I've now.... finally.... figured out the basic formula:

`Mandeldrop{init: z = 1/#pixelloop: z = z^2+(1/#pixel)bailout: |z|<4default:  title = "Mandeldrop"  center=(1.5,0)  magn=0.5  angle=270}`

Actually , very simple

and it looks like this:

That formula was a rather distorted version. I&#039;ve now.... finally.... figured out the basic formula: Mandeldrop{ init: z = 1/#pixel loop: z = z^2+(1/#pixel) bailout: |z|&lt;4 default: title = &quot;Mandeldrop&quot; center=(1.5,0) magn=0.5 angle=270 } Actually , very simple :) and it looks like this: ![567f38f459180.png](serve/attachment&amp;path=567f38f459180.png)

0

Does anyone know how to write a formula for this fractal?

I've seen it called a teardrop or mandeldrop fractal, but after much experimentation have been unable to recreate it.

There may already be a formula for this in the database, but I couldn't find one.

Inverse

The Mandelbrot doesn't exist outside a circle of radius 2 on the complex plane, this gives scope for turning it inside out by mapping z0 to 1/z0. The result, center at (1.4,0), is as follows.

&gt;Does anyone know how to write a formula for this fractal? &gt;http://www.relativitybook.com/CoolStuff/erkfractals/mandeldrop_small.gif &gt;I&#039;ve seen it called a teardrop or mandeldrop fractal, but after much experimentation have been unable to recreate it. &gt;There may already be a formula for this in the database, but I couldn&#039;t find one. Inverse The Mandelbrot doesn&#039;t exist outside a circle of radius 2 on the complex plane, this gives scope for turning it inside out by mapping z0 to 1/z0. The result, center at (1.4,0), is as follows.

TO get Instant Dissertation help UK.

-5

Happy to find here formula for this fractal. Thank you so much for sharing it.

Regards,
CV writer at CV Folks .

Happy to find here formula for this fractal. Thank you so much for sharing it. Regards, CV writer at [CV Folks](https://www.cvfolks.co.uk/) .

-5
``````Mandeldrop {
init:
z = (0, 0)
loop:
z = sqr(z) + 1/#pixel
bailout:
|z| <= @bailout
default:
title = "Mandeldrop"
param bailout
caption = "Bailout value"
default = 4.0
endparam
}
``````
```` Mandeldrop { init: z = (0, 0) loop: z = sqr(z) + 1/#pixel bailout: |z| &lt;= @bailout default: title = &quot;Mandeldrop&quot; param bailout caption = &quot;Bailout value&quot; default = 4.0 endparam } ````

0

You don't need a separate formula for this: just use the standard Mandelbrot formula, and add the Inverse transformation on the Mapping tab.

You don&#039;t need a separate formula for this: just use the standard Mandelbrot formula, and add the Inverse transformation on the Mapping tab. :)

Ultra Fractal author

0

You don't need a separate formula for this: just use the standard Mandelbrot formula, and add the Inverse transformation on the Mapping tab.

It only works with Creative Edition, so it doesn't count.

&gt;You don&#039;t need a separate formula for this: just use the standard Mandelbrot formula, and add the Inverse transformation on the Mapping tab. :) It only works with Creative Edition, so it doesn&#039;t count.

0

It only works with Creative Edition, so it doesn't count.

Really? Perhaps I'm missing the point but I'm curious. Can I ask what program version are you using... do you not have a mapping tab?

I have been able to recreate this inverse Mandelbrot figure in UF 4.04, which I think pre-dates the introduction of the creative edition, using Frederik's suggested method above. It looks very much like the figure the OP was enquiring about. It was very simple to accomplish.

``````Fractal1 {
fractal:
title="Fractal1" width=364 height=480 layers=1
credits="Frederik Slijkerman;7/23/2002"
layer:
caption="Background" opacity=100
mapping:
center=1.15437880685/-0.040077532 magn=0.87348074 angle=-90
transforms=1
transform:
p_usecenter=no
formula:
maxiter=250 filename="Standard.ufm" entry="Mandelbrot" p_start=0/0
p_power=2/0 p_bailout=128
inside:
transfer=none
outside:
transfer=sqrt filename="Standard.ucl" entry="Smooth" p_power=2/0
p_bailout=128.0
smooth=no rotation=43 index=0 color=3278080 index=182 color=13701632
index=229 color=16777215 index=258 color=16777215 index=399 color=0
opacity:
smooth=no index=0 opacity=255
}
``````

&gt; It only works with Creative Edition, so it doesn&#039;t count. Really? Perhaps I&#039;m missing the point but I&#039;m curious. Can I ask what program version are you using... do you not have a mapping tab? I have been able to recreate this inverse Mandelbrot figure in UF 4.04, which I think pre-dates the introduction of the creative edition, using Frederik&#039;s suggested method above. It looks very much like the figure the OP was enquiring about. It was very simple to accomplish. ```` Fractal1 { fractal: title=&quot;Fractal1&quot; width=364 height=480 layers=1 credits=&quot;Frederik Slijkerman;7/23/2002&quot; layer: caption=&quot;Background&quot; opacity=100 mapping: center=1.15437880685/-0.040077532 magn=0.87348074 angle=-90 transforms=1 transform: filename=&quot;Fractint.uxf&quot; entry=&quot;Inverse&quot; p_radius=1.0 p_center=0/0 p_usecenter=no formula: maxiter=250 filename=&quot;Standard.ufm&quot; entry=&quot;Mandelbrot&quot; p_start=0/0 p_power=2/0 p_bailout=128 inside: transfer=none outside: transfer=sqrt filename=&quot;Standard.ucl&quot; entry=&quot;Smooth&quot; p_power=2/0 p_bailout=128.0 gradient: smooth=no rotation=43 index=0 color=3278080 index=182 color=13701632 index=229 color=16777215 index=258 color=16777215 index=399 color=0 opacity: smooth=no index=0 opacity=255 } ```` ![5d56ee57cdedb.png](serve/attachment&amp;path=5d56ee57cdedb.png)

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

Currently using UF6.04 on Windows 10

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I believe the Express edition doesn't have transformations, whereas the Creative and Extended editions do.

Yes, the inverse mapping produces the exact same fractal. I was interested in learning how the fractal is constructed. You don't need to know that if you just want to produce the image

I believe the Express edition doesn&#039;t have transformations, whereas the Creative and Extended editions do. Yes, the inverse mapping produces the exact same fractal. I was interested in learning how the fractal is constructed. You don&#039;t need to know that if you just want to produce the image :)

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Thanks for the answer to my question, Otto. I haven't looked at the differences for so long I didn't realise the Express version was limited in this particular way.

Well, for me this was just an exercise in learning how an inside out Mandelbrot could be made... I am not a formula writer so that's as far as it goes for me!

Thanks for the answer to my question, Otto. I haven&#039;t looked at the differences for so long I didn&#039;t realise the Express version was limited in this particular way. Well, for me this was just an exercise in learning how an inside out Mandelbrot could be made... I am not a formula writer so that&#039;s as far as it goes for me! (blush)

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

Currently using UF6.04 on Windows 10

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