Author Topic: [lua] fractal zoomer (Read 11705 times)

Jens_K · « **on:** June 08, 2014, 10:46:04 am »

Hello!
During the development of my script editor I started a new project, which turned out pretty nice: A fractal zoomer for the Nspire!

I love fractals so I started reading a bit about them and finally had the urge to make a fractal renderer myself on the Nspire. I don't know if there are already fractal renderers for the Nspire, but it wouldn't bother me much because I primarily made it just for fun. Here's the result:

Features:
- Rendering of the mandelbrot set and julia sets
- It first renders at low resolution but the longer you wait, the higher gets the resolution ==> Very fast display
- Zoom in and out by clicking with the mouse
- Free adjustment of calculation depth and constants
- 7 color modes

Information:
- This program is optimized for the handheld; I don't recommend using it on the student software emulator because the emulator doesn't support partial frame updates so that it has to repaint every single pixel on every frame update, which is very slow!
- The menu sometimes doesn't work on the emulator for some reason
- I also included a feature which I haven't seen on any fractal zoomer yet: The possibility to set the values of the first segment Z₀of the sequenze of the mandelbrot set. I'm not familiar enough with fractals to say which exact mathematical meaning this has for the set, but it produces interesting "crippled" shapes (e.g. the middle-right screenshot)

Edit: This program has been revised!

I attached some awesome screenshots of both fractals in different color modes

This project is completed for me, but if you find a serious bug (on the handheld) or have a special request I'm willing to make an update.

LDStudios · « **Reply #1 on:** June 08, 2014, 12:13:53 pm »

Amazing work! You continue to do amazing things with Nspire lua, and I can't wait to see what comes next! (Hopefully an update on Jens' Script Editor

)

Streetwalrus · « **Reply #2 on:** June 08, 2014, 12:15:42 pm »

Yay. Fractals are awesome !

This looks wonderful too.

Adriweb · « **Reply #3 on:** June 08, 2014, 12:30:13 pm »

Looks very cool, and beautiful

To answer your first question, Levak made an quite optimized mandelbrot viewer in Nspire-Lua.
By optimized, I mean :
- algorithm-wise : use of quad-tree and general optimizations
- lua-wise : partial invalidates, coroutines, lua tricks etc.

Also, it's not platform-dependant (no absolute coordinates

), so it works well on all nspire platforms (but faster on TINCS and iPad, of course)

Download here (it's the "Mandelbrot_processless3.tns" file, for Lua, the rest is a C ndless program)

There is a video here (it was used for comapring to the C version, but still, you can see it running) :

Your way is quite nice too since you get to see a better "view" the longer you wait, but you get the idea quite fast

DJ Omnimaga · « **Reply #4 on:** June 09, 2014, 01:16:04 am »

THis looks very nice! I wonder how long does it take to render at decent resolution? It would be interesting to see such fractals animated and zooming in, although I doubt it could be done at full res.

Jens_K · « **Reply #5 on:** June 09, 2014, 09:53:27 am »

Thanks for the nice feedback!

@adriweb: I think mine is very optimized too; at least it seems to be not much slower as Levaks version: The same sector at 100 iterations on full resolution takes about 47.5 seconds which is only 1.5 seconds longer than levaks. Plus mine seems to render more accurate (borders seem to be more smooth on my version). I tested it with the attached "high res" version which renders at full resolution right away. Mine is also platform independent; the absolute coordinates are only for initialization; they get overwritten in the on.resize event

But I have a question about coroutines: Do they actually give advantages in speed? I mean the Nspire has only 1 core anyways...

Quote from: DJ Omnimaga on June 09, 2014, 01:16:04 am

THis looks very nice! I wonder how long does it take to render at decent resolution? It would be interesting to see such fractals animated and zooming in, although I doubt it could be done at full res.

Thanks! On average, 1/4 resolution takes about 5s; 1/2 takes about another 17s; full res takes about another 45s. So I think even on 1/4 resolution it would be too slow... But maybe it would be possible to calculate the indidual frames and afterwards display them fast enough...

Jens_K · « **Reply #6 on:** June 09, 2014, 10:15:59 am »

@LDStudios: Yes I'm still working on the update, I was just too excited about fractals

AnToX98 · « **Reply #7 on:** June 09, 2014, 11:29:43 am »

Wow so pretty

, I have to show dat to pierrotdu18

Now, Jens K -> back to the editor

Jens_K · « **Reply #8 on:** June 09, 2014, 11:34:55 am »

Quote from: AnToX98 on June 09, 2014, 11:29:43 am

Now, Jens K -> back to the editor

Aye-aye, sir!

DJ Omnimaga · « **Reply #9 on:** June 09, 2014, 12:23:35 pm »

I guess calculating individual frames then animating them pre-rendered could work for animations, although it would take a lot of space.

Eiyeron · « **Reply #10 on:** June 10, 2014, 04:35:18 am »

Do you support other fractals? It seems there is a lot of formulas that can yields pretty resutls. Here is a non exhaustive list without illustrations : http://www.lifesmith.com/formulas.html

Adriweb · « **Reply #11 on:** June 10, 2014, 09:13:22 am »

@Jens_K : I never said yours isn't optimized

Also, glad it's not platform-dependant, I guess I should have reopened the file in computer view on the software to actually see the re-init in full screen ^^

Also, the problem with Levak's version (which is probably why it's not blazing fast), is that he creates 4^n (i believe) functions for each iteration... which slows the script down.
If he solves that issue, it may be much better ^^
I don't know if he ever will though - maybe one day

(Also, I don't have any issues with the menus, like you said ?
edit : ah wait, emu... hum weird)

mdr1 · « **Reply #12 on:** June 10, 2014, 11:21:23 am »

Great that it runs on 3.1.

How to draw with the program the fractals in your post?

Jens_K · « **Reply #13 on:** June 10, 2014, 12:50:58 pm »

Quote from: Eiyeron on June 10, 2014, 04:35:18 am

Do you support other fractals? It seems there is a lot of formulas that can yields pretty resutls. Here is a non exhaustive list without illustrations : http://www.lifesmith.com/formulas.html

No, not yet... But I could give the user the ability to insert an own formula, let the math.eval function simplifyand then parse it to lua code! I'll try that when I have some spare time

Quote from: mdr1 on June 10, 2014, 11:21:23 am

Great that it runs on 3.1.
How to draw with the program the fractals in your post?

I attached a screenshot where I marked the positions of the first 5 Screenshots. Then 6th is a mandelbrot set with Z₀=0.1+0.7i; The 8th is in a Julia set with C=0.7+0.3i. The other two I can't remember or find

Oh and in case you missed it: I continue to support OS 3.1 in the latest alpha release of my script editor!

edit: Sorry, only just saw that you've already posted there...

Jens_K · « **Reply #14 on:** March 31, 2015, 10:53:08 am »

Hello again!
I had noticed that I haven't uploaded this program to ticalc yet, so in order do to that I wanted to fix a few things and polish it a bit and the inevitable happened: I became addicted to fractals again

But at least this fractal renderer now has some cool new features:

- Smooth rendering (see attached screenshot) is now selectable:
- Full color scale on emulator
- Dithering on handheld to prevent color-banding (using a 4x4 Bayermatrix)
- Support for custom fractal functions (as suggested by Eiyeron)
- Switch to page 1.2 to enter a custom function
- Uses the CAS functions of the Nspire to "extract" the required algorithms and then parses them to Lua code
- Therefore is only available on OS>3.1
- The Handheld Lua is too slow for most fractals

- Improved rendering speed, especially on emulator
- New color-set (see attached screenshots)
- Settings are now saved
- Julia sets are not rendered upside-down anymore
- Minor bug-fixes and improvements

And for the sake of the awesomeness of fractals I attached some screenshots of some nice fractals and smooth rendering

Author Topic: [lua] fractal zoomer (Read 11705 times)

Jens_K

[lua] fractal zoomer

LDStudios

Re: [lua] fractal zoomer

Streetwalrus

Re: [lua] fractal zoomer

Adriweb

Re: [lua] fractal zoomer

DJ Omnimaga

Re: [lua] fractal zoomer

Jens_K

Re: [lua] fractal zoomer

Jens_K

Re: [lua] fractal zoomer

AnToX98

Re: [lua] fractal zoomer

Jens_K

Re: [lua] fractal zoomer

DJ Omnimaga

Re: [lua] fractal zoomer

Eiyeron

Re: [lua] fractal zoomer

Adriweb

Re: [lua] fractal zoomer

mdr1

Re: [lua] fractal zoomer

Jens_K

Re: [lua] fractal zoomer

Jens_K

Re: [lua] fractal zoomer