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Offline julofi

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FFExplorer, user's formulas in VB syntax.
« on: January 10, 2022, 12:55:34 PM »
Hi
SergioCT just announced the new version 12.0 of his software FFExplorer saying only it has a new formula designer / compiler.
I will tell a bit more about it, explaining how to use it and I'll ask for help too.

GENERAL HELP REQUEST: MORE FORMULAS!
I would like that you could adapt/convert your own formulas or classic formulas to FFExplorer format using the new formula designer to be included as downloable formulas to be used in the program. The formula designer uses Visual Basic Syntax.
I will post formulas too that I have discovered myself playing with the program, to ask if they are invented and I will ask for help to adapt specific formulas too.

MINI TUTORIAL ABOUT HOW TO USE THE FORMULA DESIGNER
FFE 12.0 includes examples for the formula designer of all the main formulas in the program: Mandelbrot, Lambda, both Magnets, Manowar, all the Novas and IRFs, etc. You can open an example, v.g. Mandelbrot, look at the syntax (it uses Visual Basic, compatible with dotNet and Net5) and make changes in the formula and save it as an user's formula. You need to save a formula first to use it. One of the possible editions is changing the type of variable from Real to Complex. This way you can use complex exponents with all the main formulas of the program. Beware, you need to introduce the valours in the definition of variables or directly in the formula in the iteration loop and save it first. Then you will need to open a new canvas, choose the user's formula you just saved and begin to explore it. If you make a change in the valours of the variables in the formula designer, you need to save again the formula to be able to use it with those new variables. You can not rewrite the examples but you can rewrite by mistake the users' formulas, so use always a different name and keep that in mind.
For example, open Mandelbrot example, change variable type, add a change to the iteration loop, add a plane transformation in Previous operations. Or just adapt to VB syntax your own formula from scratch. Save it to keep it. Now save that same formula with a new name, for example TEST. Load the user's formula TEST, explore it, or make changes in the valours of the variables. Save it again with the name TEST. Now you can refresh the fractal image with F5 and see how the changes in the formula affect the image. Once you have explored your image, you can save its parameters to render it in high resolution later. The user's formula used with the values chosen for the variables will be saved in the parameters file, so you won't lose it.
I know that ideally you should be able to change the valours of all the variables without needed to save the formula first, but this is a first version and I hope that that feature is included in a new versions. Things that you can change without needing to save again the formula is: changing Initial Z, bailout and tolerance valours, iterations number, Julia mode, Juliter. But changes in exponents and other variables will require save the formula again first, with a different name if you don't want to rewrite the original formula.

PACKS TO DOWNLOAD IN THE FFEXPLORER WEB.
You can download fhe program from the section Downloads of this forum, but you have more resources available in the FFE web
https://fractalfun.es/
There are two versions of the software. One compiled with .Net (Net Framework) and another one compiled with Net5. This second one is slightly faster.
You have there a packet with 600 palettes. But you can import Fractint palettes and convert them to FFE format too. FFE cannot use Fractint palettes directly.
There is too several packets with superformulas files made by the author, myself, Gerson and other people, to be used as orbit traps in the program. There are some IFS parameters by Gerson too.

USERS' FORMULAS PACK.
And there is an all new "formulas pack" made with the formula designer, with 24 formulas so far.
Once you have learnt some basic stuff about Visual Basic syntax it quite easy to make new formulas. You don't need to know programation. I know because I compiled myself most of the formulas in that pack although I had help in some of them.
The pack includes the formulas:
- TALIS (from Ferguson's programs)
- ZPZ (created by FractRacer, an user of this forum and adapted by SergioCT)
- MIXTURE, SQUARE_TWICE, FACING A, FACING B, RINGS, TRICORN, CELTIC. That is all the formulas included in the program GAPFix Fractal, except the ones that were already included in FFE, and except the HYBRID formulas that are not compatible with this formula designer, at least no yet.
- BUFFALO, MANDELHEART, PARTIAL_BURNING_SHIP_IMAGINARY. I took the Buffalo formula from Internet. I "invented" the other two myself, just to discover the next day that they were already invented.
- BARNSLEY1, BARNSLEY2, BARNSLEY 3. Same formula for the mandelbrot and julia versions of each one. They were taken from Fractint.
- DOUBLE_MANDEL, SIMURGH, SIMURGH_DOUBLE_MANDEL. Taken from the description of the formulas in the Ultra Fractal web.
The rest of the formulas are classic transformation planes taken from the old web https://mathcs.clarku.edu/~djoyce/julia/altplane.html and a couple of new planes.

HELP REQUIRED: LAMBDA PLANES.
Lambda is often found in fractal software (such as FFExplorer) as its own independent formula, but it is in fact a plane transformation that can be applied to Mandelbrot and other formulas. I don't know how to make in the designer a transformation plane that just does that, convert Mandelbrot to Lambda. In the same way, I don't know how to do that same thing with the The 1/lambda-plane and the The 1/(lambda-1)-plane. In the pack of formulas appear as plane transformation to be applied to the Lambda formula, not as planes to be applied to a Mandelbrot formula.

The first 35 fractals in this gallery of my DeviantArt page were made using the  formula compler, from last one "JLF3304 Jungle Carpet" using the Facing B formula to the first one JLF3262 Purple Neurons that uses a variation of Talis formula. https://www.deviantart.com/jlfractals/gallery/67597013/ffexplorer






Linkback: https://fractalforums.org/index.php?topic=4590.0

Offline Alef

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Re: FFExplorer, user's formulas in VB syntax.
« Reply #1 on: January 10, 2022, 05:21:50 PM »

FFE 12.0 includes examples for the formula designer of all the main formulas in the program:
, Lambda, Manowar, etc.
USERS' FORMULAS PACK.
The pack includes the formulas:
 TRICORN, CELTIC.
- BARNSLEY1, BARNSLEY2, BARNSLEY 3. Same formula for the mandelbrot and julia versions of each one. They were taken from Fractint.
, SIMURGH, . Taken from the description of the formulas in the Ultra Fractal web.
Its surpising how software by default are repeating one an the same boring stuff like lambda and outdated formulas like barnsley or phoenix/manowar/simurg. Ducks type fractals are way better. Maybe literature are just outdated.
Some formula archivism:
https://fractalforums.org/share-a-fractal/22/some-old-stuff-maybe-fractal-nostalgia/4213
by Edgar Malinovsky aka Edgars Malinovskis.

Offline julofi

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Re: FFExplorer, user's formulas in VB syntax.
« Reply #2 on: January 10, 2022, 05:57:25 PM »
I adapted to FFExplorer most of the formulas myself. I am not the programmer, just an user with zero programming knowledge. My brain is not too big, only my head is. Big sizes for hats, but just that.
Thanks for your link, Alex, and for replying my private message last week.
I don't even know if Ducks type formula are compatible with this compiler. Could you please download and install FFExplorer, try and adapt one of those Duck formulas and show the example or tell what the program will need in its next version to make it compatible with that, and then I can try to adapt the rest myself. Half of the time I am unsuccessful.

Offline julofi

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Re: FFExplorer, user's formulas in VB syntax.
« Reply #3 on: January 10, 2022, 06:36:53 PM »
From Alex's thread with formulas.
"Szegedi butterfly" fractal
In a don't know what language: z = sqr(y) - sqrt(abs(x)) + 1i * (sqr(x) - sqrt(abs(y))) + C
In VB syntax: Z = POW(Z.imaginary,E) - POW(abs(Z.real),1/E) + New complex(0,1) * (POW(Z.real,E) - POW(abs(Z.imaginary),1/E)) + C
I have converted those SQR and SQRT in exponent variables with a default value of 2.

Checking Fractal Zoomer to see if I had gotten the formula right, I discovered that there is a Szegedi butterfly 2 formula. So, I looked inside Fractal Zoomer for the code of the formula and I found it.
z = (re(z)^2 - sqrt(abs (im(z))) ) + (im(z)^2 - sqrt(abs(re(z))))i + c
in VB syntax: Z= (POW(Z.real,E) - POW(abs(Z.imaginary),1/E)) + (POW(Z.imaginary,E) - POW(abs(Z.real),1/E)) * New complex(0,1) + C

« Last Edit: January 10, 2022, 07:23:37 PM by julofi »

Offline Alef

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Re: FFExplorer, user's formulas in VB syntax.
« Reply #4 on: January 10, 2022, 07:34:54 PM »
Ducks fractals mostly depends on colour methods not on compiler. There are lots of very simple abs using formulas revealing ducks fractals as inside julia sets with colour algorithms that build up value during iteration (lyapunov, exponent smoothing and many more).
It is an Ultra Fractal compiler language. sqr() and sqrt() is square and square root, * 1i  or flip( real_value ) creates imaginary value.

Offline julofi

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Re: FFExplorer, user's formulas in VB syntax.
« Reply #5 on: January 10, 2022, 07:51:40 PM »
Well, I discovered today what SQR and SQRT mean and I have already applied to the Szegedi butterfly formula. Instead of SQR and SQRT, I have used POW(X,E) and POW(X,1/E) so I can use the 2 in SQR and SQRT to generalize the formula, so I can use any exponent, even complex ones, instead of only 2.
i or 1i is New complex (0,1). I didn't know what flip meant and I have seen it in some formulas, so thanks for the info.
Last year I produced some pretty fractals with ducks in FFE using the Burning Ship Julia formula.
I guess that these thingies are duck or Kali?
https://www.deviantart.com/jlfractals/art/JLF2379-Purple-Horizon-842978779
https://www.deviantart.com/jlfractals/art/JLF2118-Fans-Lattice-in-Brownish-Red-831333837
https://www.deviantart.com/jlfractals/art/JLF2117-Fans-Lattice-in-Red-and-Purple-831329099
https://www.deviantart.com/jlfractals/art/JLF2114-Flowery-Double-Lattice-831217489
https://www.deviantart.com/jlfractals/art/JLF2110-Pink-and-Gold-831119640
https://www.deviantart.com/jlfractals/art/JLF2109-Spades-Pattern-831108589

Offline Alef

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Re: FFExplorer, user's formulas in VB syntax.
« Reply #6 on: January 10, 2022, 08:53:48 PM »
Yes, just like that.
I hadn't tried to generalise szegedi butterfly formula to other powers. Maybe it will show something interesting. Fractional and imaginary powers mostly have discontiniuties, these have branch cuts or something. Unlike 1,2,3 ... Not aesthetical, well maybe exept this, but it's a formula for just 1 fractal https://fractalforums.org/share-a-fractal/22/some-old-stuff-maybe-fractal-nostalgia/4213/msg30581#msg30581  Multiplication by complex (imaginary) value rotates fractal way better than complex power.

Offline julofi

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Re: FFExplorer, user's formulas in VB syntax.
« Reply #7 on: January 10, 2022, 09:07:40 PM »

[
Multiplication by complex (imaginary) value rotates fractal way better than complex power.

Something like this? Or multiplying elsewhere?
z = D(sqr(y) - sqrt(abs(x)) + 1i * (sqr(x) - sqrt(abs(y)))) + C
being D a complex number?

Offline Alef

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Re: FFExplorer, user's formulas in VB syntax.
« Reply #8 on: January 10, 2022, 09:16:11 PM »
Yes, like this, just Z*Dcomplex. At least it works nicely for ducks type. Butterfly is different, but maybe it would work there too.
Without complex numbers it would be more complex:
tempZ_x = Z_x
tempZ_y = Z_y
Z_x =  tempZ_x*realScale -  tempZ_y*imagScale
Z_y =  tempZ_y*realScale +  tempZ_x*imagScale
Kind of like one of ducks like https://fractalforums.org/share-a-fractal/22/some-old-stuff-maybe-fractal-nostalgia/4213/msg31270#msg31270

Offline julofi

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Re: FFExplorer, user's formulas in VB syntax.
« Reply #9 on: January 10, 2022, 10:11:38 PM »
I have tried to explore this Szegedi butterfly modified with a complex multiplier and I haven't had success.
I got a nice detail. This first image.
The second fractal is the fractal in Alef's signature. I hope it's correct. Can I include it in the formulas pack? With what name and information?



Offline Alef

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Re: FFExplorer, user's formulas in VB syntax.
« Reply #10 on: January 10, 2022, 10:57:37 PM »
Of corse, everything is kind of copyleft. I just hadn't figured out some good name. But there could be a better formulas, it's just my first.
in the thread:
Mandelnewton https://fractalforums.org/share-a-fractal/22/some-old-stuff-maybe-fractal-nostalgia/4213/msg29450#msg29450
Could have some problems with bailout, dual bailout seems to be best https://fractalforums.org/share-a-fractal/22/some-old-stuff-maybe-fractal-nostalgia/4213/msg31149#msg31149
Alsou some spirals: https://fractalforums.org/share-a-fractal/22/some-old-stuff-maybe-fractal-nostalgia/4213/msg31134#msg31134
Magnet 1 with more powers: https://fractalforums.org/share-a-fractal/22/some-old-stuff-maybe-fractal-nostalgia/4213/msg31088#msg31088
Slice of some big mathematical object: https://fractalforums.org/share-a-fractal/22/some-old-stuff-maybe-fractal-nostalgia/4213/msg30915#msg30915
version of newton: https://fractalforums.org/share-a-fractal/22/some-old-stuff-maybe-fractal-nostalgia/4213/msg31870#msg31870
Luna / Lyra newton: https://fractalforums.org/share-a-fractal/22/some-old-stuff-maybe-fractal-nostalgia/4213/msg32106#msg32106
These are kind of more easy. There are opposite of juliter, few julia iterations with following mandelbrot set iterations and lyapunov mandelbrot.

Offline julofi

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Re: FFExplorer, user's formulas in VB syntax.
« Reply #11 on: January 10, 2022, 11:20:11 PM »
Ok, I will try some of those formulas in the links. I cannot guarantee anything because my kung-fu is still very poor (I mean, I have been adapting formulas just 3 weeks. I don't know even how to code "Hello World").
Catalisator seems like a good name.
I have some formulas on my own too. I don't know if there are already invented.

Offline julofi

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Re: FFExplorer, user's formulas in VB syntax.
« Reply #12 on: January 11, 2022, 05:29:42 PM »
At Alex, using your formula but changing the function sinh for tan.
I have been trying most of the trigonometric functions with this formula. When I used TAN it only showed a horizontal line. Nothing of interest there, until I zoomed out an saw stuff on the sides. A bit of zooming there et voilà!
EDIT: I saw nothing there at zoom 1 because I was using a very high bailout. With bailout 4 the function TAN shows a rich fractal at default zoom.
So the formula used is Z = Z * Tan(Z) - C * C. Bailout is 4096, 256 iterations, colouration by escape, illuminated effect. Raw. Random RGB palette. No post-processing.
I am rendering at this moment a zoom of this image with the same palette, just rotated.

« Last Edit: January 11, 2022, 09:12:48 PM by julofi »

Offline julofi

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Re: FFExplorer, user's formulas in VB syntax.
« Reply #13 on: January 11, 2022, 07:12:02 PM »
As I said, same formula and parameters as the previous image. I just zoomed on the center and rotated the palette. No post-processing.

Offline gerson

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