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I was playing with the graph plotter included in Fragmentarium, and I recalled what I did with 1D Mandelbrot formula to produce fractal waves, that I later converted to sound (it sounded like wind gusts, pretty interesting). So I wanted to try some other formulas in 1D to see how their plots are...

In the formula section of Syntopia's code, I included a iteration loop and I started with Kaliset formula, that I translated to 1D this way:

f(x)=1/abs(x)+c

Then I added scaling and the 1D analogues of ballfold and boxfold as optional folding modes, to plot the standard Mandelbox or Kaliset/Mandelbox hybrids.
I also included the option for plotting the median of the values and exponential smoothing, wich I use as coloring method in most of my 2D images, and I added an Y-Axis zoom scale slider that is useful to adjust the display of the data.


Some images: 


Kaliset Julia - Final value

(http://img441.imageshack.us/img441/5727/kaliset05finalvalue.jpg)


Kaliset Julia - Exp. Smoothing

(http://img696.imageshack.us/img696/296/kalisetexpsmooth.jpg)


Kaliset+"Boxfold" Mandelbrot - Exp. Smoothing

(http://img849.imageshack.us/img849/6316/kalisetboxfoldmbrotexps.jpg)


Kaliset+"Ballfold" Julia - Final Value

(http://img683.imageshack.us/img683/3617/kalisetbfoldfinalvalue.jpg)


Mandelbox scale -1.5 - Final Value

(http://img12.imageshack.us/img12/9883/mandelbox15finalvalue.jpg)


Mandelbox scale -1.5 - Exp.Smoothing

(http://img441.imageshack.us/img441/4691/mandelbox15expsmooth2.jpg)


Mandelbox Julia - Exp.Smoothing

(http://img546.imageshack.us/img546/1789/mandelboxjuliaexpsmooth.jpg)



Sorry for the boring images  ;D - It's more interesting when you adjust the params and watch the plot changing in realtime.

Well, I made this just out of curiosity, but who knows, some parts of the plots are pretty much like soundwaves, maybe I'll try again with my VB.NET code to produce .wav files and listen how it sounds  :whistle2:.

these remind me of Tune Smithy.

it's not boring at all, i really like this  ;D

thos pictures reveal interesting properties, some are mirrored at the x axis, some truly have chaotic characteristic, i dont know what mister mandelbrot would say, but somehow those
1d plots should be used to classify the fractals, e.g. the "Mandelbox Julia - Exp.Smoothing" shows straight lines, whereas "Mandelbox scale -1.5 - Final Value" shows more "chaos"...

I posted some similar things on here a while ago, i used the regular Mandelbrot / Julia formula though, most are just the real axis of the regular Mandelbrot set, or of various Julia sets....

http://www.youtube.com/watch?v=FbXvWakB_AY

I searched the web for that program after reading your post, looks interesting.


Thanks :)



I missed that, nice sounds! The sounds I generated are in this post: http://www.fractalforums.com/new-theories-and-research/sound-wave-generation-from-1d-mandelbrot-formula/?PHPSESSID=e42b9487ecf46e070e1a3d43d947fc92
But yours are definitely better ;)





Yes, most are mirrored, except the boxfolded julias, just like happens with the 2d/3d versions. And final values plottings are always more chaotic as they are the result of the iterated function.  Exp.smoothing is statistical data based on how the values change during the iteration, so a less chaotic behavior is expected. But you are right, maybe there are some other interesting properties that can be deduced with this plots. I just posted a few, but a great variety of results can be obtained.


This is a close-up of a regular scale 2 mandelbox, exponential smoothing plotting:

(http://img21.imageshack.us/img21/5199/mandelboxscale2plot22.jpg)


Note the self-similarity of the waves, and the gap at x=1, that I guess it corresponds to the highlited area in the picture below:

(http://img515.imageshack.us/img515/231/mandelboxscale22.jpg)