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I have implemented an application for Android phones called FractView. There are already a lot of viewers/generators for fractals, in particular the Mandelbrot Set in Android but I missed some features in them and included these in my application:

You can enter your own formula. I even added support for derivations, so that it is sufficient to enter "newton(z^3-1)" for z(n+1) to get the corresponding newton fractal. It also supports nova-fractals in a similar way.

For colors, I use Palettes with cubic spline interpolation using the L*a*b color model. They can be freely edited.

The source code is available under GPLv3, so naturally I did not include ads and it is free.

I would appreciate feedback, and also, if you have some parameters that generate nice fractals, tell me, I will include them in a manual.

Congratulations :D (edit: for being the first user)

And thanks for the compliment.

Tricorn: sqr conj z + c
Burning Ship: sqr(abs zr + i abs zi) + c
Is this one Burning Bird? sqr(zr + i abs zi) + c

z(0) is 0 for all of them.

Don't forget to use different powers: (zr + i abs zi)^3 + c
And when using pinch to zoom, use three fingers to shear, so that you don't miss out these julia islands in the burning ship fractal.

Also thanks for the suggestions. I actually use Log smoothing (log nrIter + 1 + smoothing factor); but I plan to customize this in some later version.
I will look into the other suggestions soon.

Yes, thats it, thank you!

More suggestions:
1) if calculated a fractal save into memory the iteration value NOT the colorized (smooted) value. Then program would recolor the fractal fast if I choose another colorization function. "Method" function would be in "Bailout Palette" menu instead of "Bailout" menu...
2) Also don't recalculate the fractal if I choose another palette or length of palette
3) Function "pause of calculation" would be desired for less used battery capacity if I not use the program for a while (after selecting a new area and already calculated a part of it)
4) after zooming keep the resolution of already calculated place while recalculation, not create large rectangles (like in Fractiod app)
5) if I tap the fractal with one finger accidentially don't recalcute it, only if I hale it min. 10% of it's image dimension
6) (I can't set coloring gradient in convergent areas with palette length parameter) OK, it's in "Lake Palette"! :)
7) If run other app while calculating, and then click FractView's icon it starts on reseted Mandelbrot and lost my calculated fractal...
8 ) And I'm waiting for bookmarks function! :D
9) Save my functions also would be great.
10) Preset functions (burning bird and ship :) )
11) save own palettes
12) preset color palettes
13) if it is possible, save coordinates, function and coloring info into .png's tag information or header (color palette itself doesn't have to save). After that in a new "Open fractal" menu I could open the image and app load the fractal for continue the exploration.

Great program anyway, 3-finger usage is amazing! My new favorite after Fractoid for inner coloring fractal generation: http://www.fractalforums.com/new-theories-and-research/a-new-look-into-escapetime-fractals-using-abs-and-inner-coloring/ (http://www.fractalforums.com/new-theories-and-research/a-new-look-into-escapetime-fractals-using-abs-and-inner-coloring/)
(FractView images later...)

Waiting for update!

Burning bird is the last fractal here: http://fraqtive.mimec.org/features, called 'sitting bird'. [how do I add images in this forum?]. I would rather call it 'begging dinosaur' ;)

@bkercso Can you provide me with resources for first- and secound ciclois test for Mandelbrot? Thanks a lot for your suggestions.

1) This is not so easy because you would have to save the entire orbit (like for SumExp or SumDelta) for each pixel which is not possible.
But 2, 4 and 5:
I plan to add caching so that only certain portions of the image would be recalculated (for instance moving, changing colors, changing colorization of
only the lake or the escaping orbits; scaling is more difficult and might not be possible in a satisfying way).

3) This is something I would like to keep the way it is, because usually the OS reduces the thread priority of background apps, so
they don't consume that much power, and furthermore when you calculate an image that takes a long time, you might just quickly check
some emails and then want to look back whether rendering is already done (this is also why I always show the "Calculation finished"-message).

6)Yes, that's a bit confusing and it's a compromise for devices with lower resolutions where the Palette does not fit next
to the Lake-settings. But I will make it more user-friendly and put length into the Bailout/Lake-menu. Makes way more sense.

7) This is caused by Android that kills applications if it needs memory. Afaik the only solution to this would be to always run
it in foreground with a status icon (like an MP3-player). I am thinking about various other solutions for this problem like
saving the last fractal that was rendered. This would be addressed together with the bookmarks.

9, partly 10, 11, 12) These I would combine with the bookmark menu. I am thinking of something like a 'Pick from bookmarks'-button inside the dialogs which might be the least confusing way to do it. But this will take some time.

10) I actually plan having something like "phoenix, mandelbrot, burning ship, custom" in a list. This I will address in some later update, where I also plan support for custom colorizations. I will also add easy support for julia-sets with this, but this will take some time. But I will add an abs-function and a sgn-function that makes it easier to enter burning ship-alike fractals (have to find good names for those...)

13) This would be nice, true. I am not sure how to do this yet (afaik in PNG this is not possible, but it should be possible to put it as capture in the gallery?)

So, thanks a lot, again for this exhaustive list. It really is extremely helpful :)

You can add image: upload somewhere and put link between (http://kepfeltoltes.hu/130222/1145552015N_vtelen_www.kepfeltoltes.hu_.png) (se image button here).

Mandelbrot Main cardioid- and period2 circle test described in wikipedia article, in "Optimizaton" chapter (end of the article):
http://en.wikipedia.org/wiki/Mandelbrot_set (http://en.wikipedia.org/wiki/Mandelbrot_set)

13) I solved this in my fractal generator program with save a .txt when saving .png with the same name. Every info about fractal and coloring is in the text file.
Another way is pixel-coding info in the image itself. :)

My pleasure if you make a personalized fractal app for me! :D
For benchmarking please check Fractiod! This little app is really cool!

My goal was to have as natural gradients as possible. For some time I favored something like YUV, but after some research L*a*b seemed to be the best choice. I did some comparison with RGB and the result is way better.
I did not pick HSV mainly for the reasons that its parameters do not really represent natural perception (for instance the lightness of 0,1,1 =red differs a lot from 270,1,1 = blue), and when interpolating the h-parameter you have to choose whether to go left or right. For instance, when interpolating from red to cyan, you either can choose the way via yellow and green, or via blue and purple. In both cases, lightness changes in the gradient (via blue it becomes quite obvious, it becomes very dark and then brighter again), and small changes in the parameters can have big effects (if the cyan is a bit more greenish you'd get a gradient via yellow, if it's more bluish, via blue).
Still I use HSV for the color picker because it's imo the most user friendly way (try to pick some shade of gray with an RGB-color-picker on a mobile device...).

Here are some inner coloring images. These are founded in non-divergent islands, rendered with LastArc Lake-function. (With inner coloring method higher iteration number resulting more details on picture.)

Burning ship:

(http://kepfeltoltes.hu/130225/Fractal-s001_www.kepfeltoltes.hu_.png)

(http://kepfeltoltes.hu/130225/Fractal-s008_1__www.kepfeltoltes.hu_.png)

(http://kepfeltoltes.hu/130225/Fractal-s010_www.kepfeltoltes.hu_.png)

(http://kepfeltoltes.hu/130225/Fractal-s012_www.kepfeltoltes.hu_.png)

(http://kepfeltoltes.hu/130225/Fractal-s013_1__www.kepfeltoltes.hu_.png)

(http://kepfeltoltes.hu/130225/Fractal-s013_www.kepfeltoltes.hu_.png)

(http://kepfeltoltes.hu/130225/Fractal-s018_www.kepfeltoltes.hu_.png)

(http://kepfeltoltes.hu/130225/Fractal-s019_1__www.kepfeltoltes.hu_.png)

(http://kepfeltoltes.hu/130225/Fractal-s019_www.kepfeltoltes.hu_.png)

(http://kepfeltoltes.hu/130225/Fractal-s020_www.kepfeltoltes.hu_.png)

Burning bird:

(http://kepfeltoltes.hu/130225/Fractal-b004_www.kepfeltoltes.hu_.png)

(http://kepfeltoltes.hu/130225/Fractal-b011_www.kepfeltoltes.hu_.png)

(http://kepfeltoltes.hu/130225/Fractal-b014_www.kepfeltoltes.hu_.png)

(http://kepfeltoltes.hu/130225/Fractal-b015_www.kepfeltoltes.hu_.png)

(http://kepfeltoltes.hu/130225/Fractal-b016_www.kepfeltoltes.hu_.png)

(http://kepfeltoltes.hu/130225/Fractal-b018_www.kepfeltoltes.hu_.png)

I found that SumExp and SumDelta methods reach their limit earlier than LastArc method. At deeper zooms I cannot get color gradients with SumExp and SumDelta while LastArc I get:

Deep zoom (approx. 1E-8 but I don't know exactly):
SumExp:
(http://kepfeltoltes.hu/130225/Fractal-s021-SumExp_www.kepfeltoltes.hu_.png)

SumDelta:
(http://kepfeltoltes.hu/130225/Fractal-s021-SumDelta_www.kepfeltoltes.hu_.png)

LastArc:
(http://kepfeltoltes.hu/130225/Fractal-s021-LastArc_www.kepfeltoltes.hu_.png)

Deeper zooms (~5 times larger):
SumExp:
(http://kepfeltoltes.hu/130225/Fractal-s021-SumExp-zoom_www.kepfeltoltes.hu_.png)

SumDelta:
(http://kepfeltoltes.hu/130225/Fractal-s021-SumDelta-zoom_www.kepfeltoltes.hu_.png)

At less deep zoom it is not a problem:
SumExp:
(http://kepfeltoltes.hu/130225/Fractal-s017_SumExp_www.kepfeltoltes.hu_.png)

SumDelta:
(http://kepfeltoltes.hu/130225/Fractal-s017_SumDelta_www.kepfeltoltes.hu_.png)

LastArc:
(http://kepfeltoltes.hu/130225/Fractal-s017_LastArc_www.kepfeltoltes.hu_.png)

Some more interesting pics:

3rd order Burning ship ((abs(zr) + i abs (zi))^3+c:
(http://kepfeltoltes.hu/130227/Fractal-s3-002_www.kepfeltoltes.hu_.png)

(http://kepfeltoltes.hu/130227/Fractal-s3-008-oldalso_1per4_www.kepfeltoltes.hu_.png)

4th order Burning ship ((abs(zr) + i abs (zi))^4+c:
(http://kepfeltoltes.hu/130227/Fractal-s4-001_www.kepfeltoltes.hu_.png)

(http://kepfeltoltes.hu/130227/Fractal-s4-013_iter_100_www.kepfeltoltes.hu_.png)

(http://kepfeltoltes.hu/130227/Fractal-s4-015_www.kepfeltoltes.hu_.png)

Divergent islands in non-divergent area:
(http://kepfeltoltes.hu/130227/Fractal-s4-022-divergent_islands_www.kepfeltoltes.hu_.png)

General announcement: I just uploaded a new version. I put in some suggestions (caching, bookmarks, use min/max-values) and also I think that I improved usability for Transfers. Here's a list:

* Bookmarks, yes bookmarks :D

* Caching: Values are kept so that changing colors, and also transfer + transfer range, does not require recalculating the whole image. Parts of the cache are kept when moving the image or changing the number of iterations. Also, convergent points are kept when you just pick a different Method for divergent points.

* Moved 'length' from palette into 'transfer' as Min-Max-values. Also, added a menu to pick transfer method.

* Automatically set the range of colors. This can be done by unselecting "Custom Range" in the transfer menu.

* Sharing + Set as Wallpaper in Save-menu.

* Last fractal is stored when the application terminates, and reused when restarting.

* If you accidentially tab the screen, you got 1/6 seconds to untab it.

* For Burning Ship, there is a new function "cabs" that is defined as follows: cabs p = abs re p + i abs im p. So, burning ship now becomes "sqr cabs z + c". There is also a "polar"-function (for those who remember it from FractInt)

* When you add a new color, a random color is generated.

* Instead of "zn1" use "z1" to access the last element in orbit.

* For arguments with multiple parameters, I now use a more LISP-like syntax (for 99.9% of functions, this is irrelevant, but for Nova fractals the syntax now is "nova (x^3-1) ; 1 ; 2".

Please to all my users :D keep me posted on bugs and suggestions, and tell me about crashes. Concerning bookmarks: I will eventually add a menu to delete and rename bookmarks, and also to just pick certain aspects of a bookmark.

Excellent work, my man! :) This is really useful!
~~Moreover these new features a multiple factor for color cicling would be desired.~~ Ok, I got it: I have to edit one of Transfer-Costum range upper or lower limit.

Thanks again for this app!

EDIT:
- number 19) bug is still actual
- 20) Idea: 2 sliders would be helping recoloring: one slider increase/decrease Lake coloring range (eg. upper limit), and another would be for Bailout. The one button for these 2 sliders would be next to bookmark button. (For Lake Last_Arc the scale would be log scale between 1E-8..1E3
- 21) full screen Bookmarks menu with multiple rows and/or columns; Delete Bookmark function
- 22) save bookmarks with saved images (eg. in same directory, with same filename)

What variable precision did you use? 12 digits?

ad 19. Hm, I cannot reproduce it. So, if for instance the epsilon-value shows like 1e-9, you cannot change it to 1e-12? On my nexus 7 and htc evo this works. Which Android-version is it?

- 21) full screen Bookmarks menu with multiple rows and/or columns; Delete Bookmark function
- 22) save bookmarks with saved images (eg. in same directory, with same filename)

Both are nice ideas, at least delete bookmarks should be available soon, also saving the text-file together with an Import-function would be nice.

What variable precision did you use? 12 digits?

Well, in Android you are pretty much bound to 64 bits, so around 12-13 digits. Arbitrary precision or higher precision would of course be nice, but very slow on mobile devices (and also in Java). I don't think that the problem is within the color gradient (otherwise you would see similar structures also for last_angle.).

"1/SumRelativeDelta method and I can make zoom of 1E16 times with 20 digits variables" Which programming language and data structures are you using and do you have an example for 1/SumRelativeDelta? I am always searching for new colorization methods :)

No, in formula "1E-9" mantissa is "1". I can edit "-9" but cannot edit "1" (I tried it in color range fields).

Ok, this precision on mobiles is OK, no need more of course. Just I would like to know. :)

My colorization method is:

Code:

z=abs(z)^2+c (or whatever formula you want to use)
mold=m
m=sqrt(|z|)
[b](if m>1E-10 (or 1E-X, try it) then)
sum:=sum+abs(mold-m)/m[/b]

Please find pics on the link above, 2nd half of the page (http://www.fractalforums.com/new-theories-and-research/a-new-look-into-escapetime-fractals-using-abs-and-inner-coloring/ (http://www.fractalforums.com/new-theories-and-research/a-new-look-into-escapetime-fractals-using-abs-and-inner-coloring/)).

And what is your opinion about "color density sliders" suggested in previous post? For inner coloring this is needed indeed, because if I change iteration number color density is change significantly (!).
It would be enough if I could adjust color cycling number with 1 slider for Lake coloring, when Costum range is ON. :) (Log slider, values between 0.1..10 or somewhat similar.)

No, in formula "1E-9" mantissa is "1". I can edit "-9" but cannot edit "1" (I tried it in color range fields).

Ah, now I get it. This seems to be a bug with Android's implementation of EditText, or I am supposed to not use decimals with an E at all... I will try to figure it out...

Thanks for the colorization, maybe I will add it in one of my next updates (with your permission of course).

And what is your opinion about "color density sliders" suggested in previous post?

I hope I don't misunderstand your proposal: If changing iterations is changing the range of values, it is a good idea to use the log-transfer to lower this effect (this is usually enough for me).
From a usability point of view I am not sure how to implement such sliders in a satisfying and intuitive way. Putting a slider somewhere would add complexity (also considering that it is only active when there is a checked checkbox inside some hidden menu, which would be unintuitive to users, especially on small devices). So, I would not currently see a possible userfriendly way that would not double functionality or increase the over-all complexity of the application (but of course, I tend to change my opinion).

"Thanks for the colorization, maybe I will add it in one of my next updates (with your permission of course)."
Permission allowed and big thx! :)

About sliders:
Ok, I will try Log transfer. But it resulted different pics, maybe I would like to use normal transfer too.
Yes, iteration changes values, this causes the colorization mismatch.
I thinked about make a button next to Share button, and it pops up a menu with two sliders (for Lake and Bo). Whith these sliders you can adjust the value range of the palettes. This would be very helpful for me at Lake coloring; Bo coloring requires this only when you are close to the borderline of non-divergent islands. But in those cases slider's function really needed.

If Costum range checkbox is inactive, repeat number of palette would be different from 1 too. You could edit this number with suggested sliders, that is the matter. :)

And some more pics ;D :

(cabs z)^5 + c, inner coloring (non-divergent araes)

low-detailed non-divergent island (blue ones)
(http://kepfeltoltes.hu/130320/Fractal-s5-016_www.kepfeltoltes.hu_.png)

(http://kepfeltoltes.hu/130320/Fractal-s5-006_www.kepfeltoltes.hu_.png)

(cabs z)^4 + c, inner coloring (non-divergent araes)

borderlines
(http://kepfeltoltes.hu/130320/FractView___cabs_z__4___c__at_-1_23072__0_00545_2__www.kepfeltoltes.hu_.png)

a zoom out
(http://kepfeltoltes.hu/130320/FractView___cabs_z__4___c__at_-1_23072__0_00545_www.kepfeltoltes.hu_.png)

(http://kepfeltoltes.hu/130320/FractView___cabs_z__4___c__at_-1_23074__0_00541_www.kepfeltoltes.hu_.png)

(http://kepfeltoltes.hu/130320/FractView___cabs_z__4___c__at_-1_23075__0_00518_www.kepfeltoltes.hu_.png)

divergent islands
(http://kepfeltoltes.hu/130320/FractView___cabs_z__4___c__at_-1_25239__0_00009_www.kepfeltoltes.hu_.png)

cells
(http://kepfeltoltes.hu/130320/FractView___cabs_z__4___c__at_-1_25242__0_00009_2__www.kepfeltoltes.hu_.png)

a zoom out
(http://kepfeltoltes.hu/130320/FractView___cabs_z__4___c__at_-1_25242__0_00009_3__www.kepfeltoltes.hu_.png)

and the last one (sorry, I tried selecting... :) )
(http://kepfeltoltes.hu/130320/FractView___cabs_z__4___c__at_-1_25242__0_00009_www.kepfeltoltes.hu_.png)

I tested the high resolution feature (max 2048x2048 pixel). Generated this 2.4 Mpixs. image on a ZTE Grand X In (1,6 GHz Intel Atom) during 1 hour; 440 iterations/pixel, (cabs z)^4 + c. It used 75% of battery power.

(http://kepfeltoltes.hu/130326/FractView___cabs_z__4___c__at_-0_38636__1_18393_5__www.kepfeltoltes.hu_.png)

The color palettes and editor are really nice and easy to use. My own little pascal fractal generator don't contains palette editor (only linear interpolation between loaded palette's colors).
Searles, did you think about an export palette feature? ::) It could save palette into 1x1000 pix .bmp file. It could help anyone who write his own program but hasn't large experience in graphical program development tools...

Wow, this last picture is a real beauty. What I am definitely planning is to export picture-data so that people can share specifications; for exporting palettes, I will try to add a colorization that allows this, like in the following way: Pick a range in the resize-menu and pick scale
1, 0 | 0.5;
0, 1 | 0.5
and function "x", and a certain colorization.

I wanted to do something like this in order to also view complex functions (I have implemented 2-dimensional color palettes, this will be a cool thing in a later update), and it will be useful for exactly what you want.

I am currently working on my phd thesis (which currently has super-top priority), but I will try to put in an update by end of April where I will try to address some of your issues:
https://code.google.com/p/fractview/issues/list

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Fractal Software => Smartphones / Mobile Devices => Topic started by: searles on February 21, 2013, 01:18:54 PM