### Lyapunov Pagoda

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#### ThunderboltPagoda

• Fractal Furball
• Posts: 236

#### Lyapunov Pagoda

« on: August 19, 2019, 03:24:43 PM »
My Lyapunov program "Lyapunov Pagoda" is released now. I'm neither a mathematician nor a professional coder, so don't expect too much! The major drawback of Lyapunov Pagoda is, that only single precision is supported. For more information about the program, see the enclosed readme.txt.

It's available in 32 and 64 bit for Windows. If you are using Linux or MacOS and try it with wine, please tell us the results. It has been tested with Ubuntu, and it worked, but there was a minor issue with changing the styles.

Current version: 1.1.2.0
Released: 2020-04-26

Thanks to marcm200 for beta testing, and to Gerson for some remarks and suggestions!

« Last Edit: April 26, 2020, 12:55:43 PM by ThunderboltPagoda »

#### ThunderboltPagoda

• Fractal Furball
• Posts: 236

#### Re: Lyapunov Pagoda

« Reply #1 on: August 19, 2019, 05:28:23 PM »
New version: 1.0.0.3

Just a tiny update: Added mouse wheel support for vertical scrolling on Gerson's request.

#### gerson

• Fractal Flamingo
• Posts: 337

#### Re: Lyapunov Pagoda

« Reply #2 on: August 19, 2019, 07:10:56 PM »
Don't worry about users. I think if you like to use it is enogh.
I am enjoing to play with it. Keep doing.
Some images.

#### gerson

• Fractal Flamingo
• Posts: 337

#### Re: Lyapunov Pagoda

« Reply #3 on: August 20, 2019, 06:55:15 PM »

#### gerson

• Fractal Flamingo
• Posts: 337

#### Re: Lyapunov Pagoda

« Reply #4 on: August 21, 2019, 03:49:01 PM »
Some suggestions:
1 - One option to post your program is in this thread. See what mrrudewords did with Infinity Fractal. All history is on this thread:

2 - Maybe you could port marcm200's formulas from his software lyapunov-core to Lyapunov Pagoda. It would be a way to give windows interface to that good program.
https://fractalforums.org/programming/11/lyapunov-image-software/2954
It was released under  GPL-3.0:
https://github.com/marcm200/lyapunov-core

3 - Register the version of the program on "About tab" under "Options" and inside the parameter file to control when it would be loaded in other version that it was done.

#### ThunderboltPagoda

• Fractal Furball
• Posts: 236

#### Re: Lyapunov Pagoda

« Reply #5 on: August 21, 2019, 04:52:54 PM »
Some suggestions:
1 - One option to post your program is in this thread. See what mrrudewords did with Infinity Fractal. All history is on this thread:

mrrudewords postet all previous versions of his program as attachments in his thread here, but I don't want to make all versions of Lyapunov Pagoda available for long-term. Only the current version will be available. And mrrudewords's current version, which is always linked in the first posting of his thread, is not an attachment. It is in the download section of the forum, and this is exactly what I wanted for Lyapunov Pagoda, too. But you can't post there without special permission from the forum admins, and I didn't get that permission though I asked for it. So for the time being, my own web space will be the download site for the program.

Quote
2 - Maybe you could port marcm200's formulas from his software lyapunov-core to Lyapunov Pagoda. It would be a way to give windows interface to that good program.
https://fractalforums.org/programming/11/lyapunov-image-software/2954

Well, I won't "steal" his formulas, and to make the program more user-friendly, someone (e.g. Marc himself) could write a simple wrapper which translates GUI input into command line parameters. That would be pretty easy, I think, but it's not my job.

But I have good news for you: I have Mario Markus' book "Die Kunst der Mathematik" (available in German only), and there are a lot of additional formulas I can make use of. I'm sure I will add some of them in a future release of Lyapunov Pagoda, and maybe some of these formulas are similar or identical to Marc's.

Quote
It was released under  GPL-3.0:
https://github.com/marcm200/lyapunov-core

I know, I have already used the program. But I don't want to give away my source code (well, very bad programming style, you know ...  ), and that means that a license with strong copyleft (like GPL) is not good for me.

Quote
3 - Register the version of the program on "About tab" under "Options" and inside the parameter file to control when it would be loaded in other version that it was done.

Well, I don't see a strong need for a "About" tab, because you can make a right click on the exe file and see the program version in the "details" tab. Anyway, I will add "About" to the menu. Regarding the metadata files: You will always be able to import any of the files into any program version. But I can add the version info below the parameter lines, that is no problem.

#### marcm200

• Fractal Freak
• Posts: 677

#### Re: Lyapunov Pagoda

« Reply #6 on: August 21, 2019, 05:37:09 PM »
Well, I won't "steal" his formulas
Of course you can use the formulas if you find something interesting for your purposes. They weren't found by a specific intelligent method, just randomly adding terms until it got too complicated to manually optimize the calculation path.

f(x) is the iterating function, g is the function used for calculating the Lyapunov exponent, in the classical case g=f, in the detached case, anything (like you did with your July Iotm entry "Filigree ball factory").

Code: [Select]
f(x)=b*sin(x+r*cos(x+r)), g=f'f(x)=b*sin(x+r)*sin(x-r), g=f'f(x)=b*sin^2(x+r), DETACHED g=r-2rx <> f'f(x)=b*sin(x+r)+b*sin^2(b*x+r), DETACHED g=sin^2(x+r*b)-r*x <> f'f(x)=r*sin^2(x-r)+b*sin^3(x+2r), DETACHED g=rx-b*sin^4(rx-b) <> f'f(x)=r*sin(x)*(1-b*sin(x+r)), g=f'f(x)=b*atan((x+r)*sin(x+r)), g=f'`
and to make the program more user-friendly, someone (e.g. Marc himself) could write a simple wrapper which translates GUI input into command line parameters. That would be pretty easy, I think, but it's not my job.
Well, I'm not very good at GUIs to say the least (the farthest I got was with the domino-computer program I posted), in fact I stopped learning about them when I came across all those abstraction layers of layers of layers for just getting a pixel onto the screen (only talking about Windows and C++ here).

#### gerson

• Fractal Flamingo
• Posts: 337

#### Re: Lyapunov Pagoda

« Reply #7 on: August 22, 2019, 06:03:30 PM »
@ThunderboltPagoda About suggestions, keep what you want and all others feel free to discart.
I like the program because it give nice images (some like abstract art) and run fast on my computer (that is old).
More images...

#### ThunderboltPagoda

• Fractal Furball
• Posts: 236

#### Re: Lyapunov Pagoda

« Reply #8 on: August 26, 2019, 04:46:31 PM »
New version: 1.0.0.4

New:

- "Set Back" button for coordinates
- "About" tab in the menu, provides version information and an email link to the author (i.e. to me)
- version information stored in metadata files
- several new iteration formulas from marcm200 (thanks for that)

My favourite among the new formulas is f(x) = b*sin(x+r)*sin(x-r), which can produce beautiful ornaments (see attached image).

#### gerson

• Fractal Flamingo
• Posts: 337

#### Re: Lyapunov Pagoda

« Reply #9 on: August 26, 2019, 08:57:02 PM »
Liked very much new version. "Set back" button help a lot to explore the images.
Thanks for including new formulas.

#### gerson

• Fractal Flamingo
• Posts: 337

#### Re: Lyapunov Pagoda

« Reply #10 on: August 27, 2019, 03:16:49 PM »
yesterday I forgot to thank marcm200 too.
More images: intersection and bird.

#### ThunderboltPagoda

• Fractal Furball
• Posts: 236

#### Re: Lyapunov Pagoda

« Reply #11 on: August 28, 2019, 11:55:59 AM »
More images: intersection and bird.

Nice. A companion for the eagle-owl and the swan.

#### gerson

• Fractal Flamingo
• Posts: 337

#### Re: Lyapunov Pagoda

« Reply #12 on: September 02, 2019, 09:23:05 PM »
I tried to reproduce a marcm200's image using Lyapunov Pagoda and lyapunov-core (that is the program I suppose marcm200 used to render his image).
Original image:
www.deviantart.com/marcm200/art/ldd76-Red-dragon-788167518
Colors are different because I hadn't the lyapunov-core parameter. See the result.

#### marcm200

• Fractal Freak
• Posts: 677

#### Re: Lyapunov Pagoda

« Reply #13 on: September 03, 2019, 09:30:46 AM »
Colors are different because I hadn't the lyapunov-core parameter. See the result.
Yes, the colors make all the difference. I attached two parameter files: the red dragon with its original color (lyapunov-core) and a version, where the dragon is gone (same calculated exponents, color interval limits moved around a bit).

#### julofi

• Fractal Feline
• Posts: 152

#### Re: Lyapunov Pagoda

« Reply #14 on: September 09, 2019, 05:52:20 PM »
I just tried this software today. I don't have experience with Lyapunov fractals.
This is my first image with Pagoda. The title of the image is "Grass and Wind".

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