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gfx/fract/LyapModules.lha

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Showing:m68k-amigaosppc-amigaosppc-morphosi386-arosi386-amithlonppc-warpupppc-powerupgeneric
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Short:Lyapunov modules for ZoneXplorer
Author:Elena Novaretti (elena [AT] elenadomain [DOT] it)
Uploader:elena elenadomain it
Type:gfx/fract
Version:1.0
Requires:gfx/fract/ZoneXplorer.lha
Architecture:ppc-morphos; m68k-amigaos
Date:2013-11-29
Download:http://aminet.net/gfx/fract/LyapModules.lha - View contents
Readme:http://aminet.net/gfx/fract/LyapModules.readme
Downloads:830

PREMISE:
--------

NO - I'm not back, sorry =)  At least... until they will suck money for a dead
pltfrm.
But even after that... not likely.
Just, I recently had a chat with an old friend, and he told me he's still
playing
with my old good proggy ZX, still appreciating and loving it. And I realized I
never
uploaded these additional modules to Aminet - indeed, they were just on my old
site,
which I removed since long ! So here're them, if you missed them !
However, for those who may be interested... my old Fractal Gallery is still
online
at this "secret" (well, not quite ;) address: www.elenadomain.it/EFG
There's also a new section with a new kind of fractals, which was previously
unpublished. And no, sorry, I can't publish those (and other) modules since
they're
definitely not user friendly, they're for experts only (read: you wouldn't enjoy
them
so much).


INSTRUCTIONS: PLEASE READ !
---------------------------

·What's inside ?

These are two experimental Lyapunov modules for ZoneXplorer (both 68K and PPC
MorphOS
compiled mods are included).
The formula used is the classic x->rx(1-x), real numbers, with r alternating
between the plane's x and y values depending on a user-defineable binary mask.

·Installation

You may copy the Lyap directory to your ZoneXplorer/Modules dir (or just leave
it in RAM:, try the modules from there and then decide :-D)

·What about Lyapunov fractals ?

The so called "Lyapunov" fractals were strange, non-2D-coherent, filiform
chaotic
pictures computed by iterating a nonlinear formula in the Real domain, like the
original quadratic formula x->rx(1-x), where 'x' is the iteration variable and
'r' a
parameter. I wrote "non-2D-coherent" for the process being 1-dimensional and
using
real numbers, but it is "forced" to be 2-dimensional because of the way it is
represented on the 2D plane of parameters: the graphic result won't thus have a
2-dimensional coherent geometry as most other fractals have, where a complex
number or
an explicit 2-dimensional process is iterated instead.

Any initial value of 0<x<1 will converge to a same attractor, which can be a
single
point, a finite set of points or a fractal set, depending on r. For every x,y
point on
the plane, an r is passed at any new iteration which is either r=x or r=y,
depending on
an user-specified binary mask, and so on cyclically. Many iterations are
allowed, in
order for the iterative dymanic to stabilize on his 'destiny', and a value is
then
computed (the so called Lyapunov's exponent) whose value is someway indicative
of how
much ordered or chaotic the attractor is. Tricky, ways less "elegant" than
conventional
dimensional-coherent dynamics I usually like to explore; but that is, not my
invention.
The resulting pictures are however sometimes quite evocative, depicting a magic
space
inhabitated by surreal presences resembling ghost ships and magic birds in fly;
so
I also decided to implement this kind of proceedings into some ZoneXplorer
modules.
I published just a couple of them for now: from an artistic viewpoint, you won't
get so different results by changing the formula, believe me... also,
x->rx(1-x), which
is the originally suggested formula for Lyapunov fractals, is QUALITATIVELY
identical
to most other similar quadratic functions: using x->x²+r won't lead to
qualitatively
different scenarios, so as a plot of z->cz(1-z) on the complex plane will give
you
pretty the same structures making up a Mandelbrot set - more or less. OTOH,
using
higher degree polynomials, fractionals or transcendent functions usually leads
to
total chaos - nothing being worth to play with, be sure.

·Usage

Please note that these modules, as in my habit, do add extra color to the
pictures
which is NOT the result of a pre-computed palette application, but which tries
to
exploit the process dynamic to some extent (I didn't follow the traditional way
of
computing the Lyapunov exponent straightly), yet trying to keep that "Lyapunov
look
and feel"

These are experimental modules so the way parameters are used may look a bit
cryptic.

Map mode: JULIA MODE has to be ALWAYS used and is set by default (meaningless
pictures
          will be generated otherwise)

Cx, Cy:   are treated as integers and get the following meaning:
          Cx is Mask and Cy is Mask Length LESS ONE
          An OFF bit is for "A" and an ON bit is for "B".
          Example: to obtain BBABA you must set Cx = 2+8+16 = 26  and  Cy = 5-1
= 4
          Example: AAAAAABBBBBB is Cx = 63 and Cy = 11

Thresold: once more controls the color diffusion depth (more like a contrast
          control here)

Iters:    as explained previously, you will need LOTS of them, even thousands,
when
          wanting more details and for the background "noise" to disappear.
          I suggest using as few as needed to navigate, adding more and more to
zoom
          into littler details, then THE MOST ITERS YOU CAN AFFORD, when you're
sure
          you want to render your zone in high res (maybe you also want to use
the
          anti-alias option, but only if your picture is not intended for
printing !)
         

COPYRIGHT NOTICE
----------------

As for all ZoneXplorer modules, the images generated with the included modules
cannot
be used for _any commercial or promotional purpose_ without the author's written
permission. In any other cases, you're free to publish or use them the way you
want, as
long as you will include a short copyright notice about them being made with a
software
which is free but still under my copyright.

© ELENA NOVARETTI 2004-2013 - www.elenadomain.it
-------------------------------------------------


Contents of gfx/fract/LyapModules.lha
PERMISSION  UID  GID    PACKED    SIZE  RATIO METHOD CRC     STAMP     NAME
---------- ----------- ------- ------- ------ ---------- ------------ ----------
[generic]                   76      76 100.0% -lh0- 1d5d Oct  7  2003 LyapModules/Lyap/LyapColorRx1-x_1/BogusAngleHiIt.zone
[generic]                   76      76 100.0% -lh0- 265b Jun 19  2003 LyapModules/Lyap/LyapColorRx1-x_1/BogusSplash.zone
[generic]                   76      76 100.0% -lh0- fd4a Sep 28  2004 LyapModules/Lyap/LyapColorRx1-x_1/ClassicHauntedHollander.zone
[generic]                   76      76 100.0% -lh0- b86d Feb  6  2003 LyapModules/Lyap/LyapColorRx1-x_1/Crepe.zone
[generic]                   76      76 100.0% -lh0- 00a3 Feb  7  2003 LyapModules/Lyap/LyapColorRx1-x_1/Dancer.zone
[generic]                   76      76 100.0% -lh0- dee2 Sep 28  2004 LyapModules/Lyap/LyapColorRx1-x_1/Default.zone
[generic]                   76      76 100.0% -lh0- e6df Feb  7  2003 LyapModules/Lyap/LyapColorRx1-x_1/Eighty.zone
[generic]                   76      76 100.0% -lh0- e30b Sep 28  2004 LyapModules/Lyap/LyapColorRx1-x_1/FlyFlot.zone
[generic]                   76      76 100.0% -lh0- 7f21 Sep 28  2004 LyapModules/Lyap/LyapColorRx1-x_1/Hole.zone
[generic]                 1869    1869 100.0% -lh0- 3e23 Sep 28  2004 LyapModules/Lyap/LyapColorRx1-x_1/Module.68k.mod
[generic]                 9768   10311  94.7% -lh5- 7eca Sep 28  2004 LyapModules/Lyap/LyapColorRx1-x_1/Module.ppc.mod
[generic]                   76      76 100.0% -lh0- d3ae Feb  7  2003 LyapModules/Lyap/LyapColorRx1-x_1/NiceScape.zone
[generic]                   76      76 100.0% -lh0- 4366 Feb  6  2003 LyapModules/Lyap/LyapColorRx1-x_1/NiceScape2.zone
[generic]                   76      76 100.0% -lh0- 4c93 Feb  6  2003 LyapModules/Lyap/LyapColorRx1-x_1/NiceScape3.zone
[generic]                   76      76 100.0% -lh0- ce48 Feb  6  2003 LyapModules/Lyap/LyapColorRx1-x_1/NiceScape4.zone
[generic]                   76      76 100.0% -lh0- 2dac Oct  8  2003 LyapModules/Lyap/LyapColorRx1-x_1/Pinnacle.zone
[generic]                   76      76 100.0% -lh0- 316a Feb  7  2003 LyapModules/Lyap/LyapColorRx1-x_1/Swallows.zone
[generic]                   76      76 100.0% -lh0- 6372 Oct  7  2003 LyapModules/Lyap/LyapColorRx1-x_1/Trinchetto.zone
[generic]                   76      76 100.0% -lh0- dd06 Feb  6  2003 LyapModules/Lyap/LyapColorRx1-x_1/VeryNiceScape.zone
[generic]                   76      76 100.0% -lh0- 22cb Oct  7  2003 LyapModules/Lyap/LyapColorRx1-x_1/VeryNiceScapeZoom.zone
[generic]                   76      76 100.0% -lh0- 80d8 Oct  8  2003 LyapModules/Lyap/LyapColorRx1-x_2/Bounded.zone
[generic]                   76      76 100.0% -lh0- b9e7 Feb  6  2003 LyapModules/Lyap/LyapColorRx1-x_2/Bridge.zone
[generic]                   76      76 100.0% -lh0- cefc Sep 28  2004 LyapModules/Lyap/LyapColorRx1-x_2/ClassicSwallowsPoker.zone
[generic]                   76      76 100.0% -lh0- 52cc Feb  7  2003 LyapModules/Lyap/LyapColorRx1-x_2/Creatures.zone
[generic]                   76      76 100.0% -lh0- 3940 Sep 28  2004 LyapModules/Lyap/LyapColorRx1-x_2/Default.zone
[generic]                   76      76 100.0% -lh0- 0952 Oct  8  2003 LyapModules/Lyap/LyapColorRx1-x_2/Flyer.zone
[generic]                   76      76 100.0% -lh0- bd93 Feb  6  2003 LyapModules/Lyap/LyapColorRx1-x_2/Glacier.zone
[generic]                   76      76 100.0% -lh0- e3d0 Oct  7  2003 LyapModules/Lyap/LyapColorRx1-x_2/Inside.zone
[generic]                 1935    1935 100.0% -lh0- 15c8 Sep 28  2004 LyapModules/Lyap/LyapColorRx1-x_2/Module.68k.mod
[generic]                 9977   10395  96.0% -lh5- cdfe Sep 28  2004 LyapModules/Lyap/LyapColorRx1-x_2/Module.ppc.mod
[generic]                   76      76 100.0% -lh0- ea30 Oct  7  2003 LyapModules/Lyap/LyapColorRx1-x_2/Scape.zone
[generic]                   76      76 100.0% -lh0- e943 Feb  6  2003 LyapModules/Lyap/LyapColorRx1-x_2/Scape2.zone
[generic]                   76      76 100.0% -lh0- 59f0 Feb  7  2003 LyapModules/Lyap/LyapColorRx1-x_2/Scape2det.zone
[generic]                   76      76 100.0% -lh0- 40ac Oct  7  2003 LyapModules/Lyap/LyapColorRx1-x_2/Scape3.zone
[generic]                   76      76 100.0% -lh0- 804f Feb  7  2003 LyapModules/Lyap/LyapColorRx1-x_2/Scape_det.zone
[generic]                   76      76 100.0% -lh0- fc76 Feb  7  2003 LyapModules/Lyap/LyapColorRx1-x_2/Swallow.zone
[generic]                 2957    5907  50.1% -lh5- e911 Nov 29  1980 LyapModules/LyapModules.readme
---------- ----------- ------- ------- ------ ---------- ------------ ----------
 Total        37 files   28938   32849  88.1%            Nov 29 18:03

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