• September 19, 2021, 01:38:37 AM

Recent Posts

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1
Other / Re: Explore fractals (inflection tool)
« Last post by gerson on Today at 12:47:35 AM »
Great improvements, liked very much new layout.
2
Share a fractal / Re: Some old stuff, maybe fractal nostalgia
« Last post by gerson on Yesterday at 11:50:08 PM »
each time more interesting...
3
Xenodream / Re: Sharing parameter-files Jux software.
« Last post by gerson on Yesterday at 11:48:52 PM »
lot of fun with your par, thanks.
4
Forum Help And Support / Re: FRACTALARTCONTESTS.COM refuses to connect.
« Last post by 3DickUlus on Yesterday at 09:39:02 PM »
 WWW.FRACTALARTCONTESTS.COM has nothing to do with FRACTALFORUMS.ORG

sorry, nothing I can do about that.
5
Share a fractal / Re: Jim Muth Snaketree
« Last post by Alef on Yesterday at 08:08:04 PM »
Formula:
z=(-z)^1.095 + C

Jim Muth's original version:
z=(-z)^1.095 + 3.4

Not very remarkable but there are some (few) nice julia sets. It looks somewhere like ducky or glynn formula but are cutted. z=abs(z) placed before would make this in something like Ducks formula.
6
Programming / Arbitrary precision Java
« Last post by superheal on Yesterday at 07:55:18 PM »
Is there any performant arb precision lib other than Apfloat for java? I currently trying to speed up the reference calculation.
Or maybe I could use Apfloat in order to store the center and magnification parameters, but then use something different during the reference iteration that is faster?
Do you have any suggestions? I know that most of you are using c++, except of Botond who used a mixture of java and c++.
7
Share a fractal / Re: Jim Muth mandelbrot version
« Last post by Alef on Yesterday at 07:52:37 PM »
More of fractal archivism....
Jim Muth formula.
Quote
MandelbrotBC3 {
; by several Fractint users
; and then modified by Jim Muth
Then I refined or maybe destiled it till this:

*   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *
global: ;//calculate once, counter of 1/3 is the only changable parameter
float power = @thirds/3

Initial conditions:
Z = #pixel
C = #pixel

Iteration loop:
Z = log(Z)
  IF( imag(Z) > 0 )
  Z = Z + 1i*2*PI
  ENDIF
Z = exp( power*( Z + 1i*2*PI ) ) + C
*   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *

1i - imaginary unit
PI - number π as defined in Ultra Fractal


I don't understand mathematics of this, what does number Pi is doing there and what do conditionals. But it works nicely making something like log or barnsley (cuted) fractals.

Power: 2, 3, 4, 5... ordinary multi power mandelbrot set.
Power: 1.3333   1.6666666666666, 2.33333333333333,  3.6666666666666666  - cuted (non smooth) but symmetric sets.
(So powers could be represented by 1/3. Of these default power = 5/3 could be the most remarkable. Placing abs before a log creates lots of burning ships of different orientation in space.)

*   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *
So
Z = Z^power + C
equals to
Z = log(z)
Z = exp ( z* power ) + C



Ultra Fractal:
Code: [Select]
JMuthFractint {
; by several Fractint users
; and then modified by Jim Muth
;...
; and then refined or destiled by Edgars Malinovskis

global:
float power = @thirds/3

init:

IF (@settype=="Mandelbrot")
Z = #pixel
C = #pixel
ELSE
Z=#pixel
C=@julia
ENDIF

loop:
Z = log(Z)
  IF(imag(Z)>0)
  Z = Z + 1i*2*PI
  ENDIF
Z = exp(power*(Z + 1i*2*PI ))+ C

bailout:
|Z|<@bailout

default:
title = "JMuthFractint Formula"
periodicity = 0
method = multipass

float param bailout
caption = "Bailout Value"
default = 772000
min = 0
hint = "This parameter defines how soon an orbit bails out while iterating."
endparam

float param thirds
caption="Power by thirds"
default=5

endparam

param settype
caption="Set type"
default=0
enum="Mandelbrot" "Julia"
endparam

param switchsettype
caption = "switch to"
default = 1
enum = "Mandelbrot" "Julia"
visible = false
endparam

  complex param julia
    caption="Julia Seed"
    default=(1.4, 0)
    visible = (@settype=="Julia")
  endparam

switch:
type="JMuthFractint"
bailout=bailout
thirds=thirds
julia = #pixel
settype=switchsettype
switchsettype=settype
}
8
Other / Re: Explore fractals (inflection tool)
« Last post by Dinkydau on Yesterday at 07:00:16 PM »
New version: ExploreFractals_9.exe
Available in the downloads section: https://fractalforums.org/index.php?action=downloads;sa=view;down=21
The program is now also available for download at github.com: https://github.com/DinkydauSet/ExploreFractals/releases

Changes:
   1. new GUI made with Nana. This includes tabs, history and keyboard shortcuts.
   2. "Largest circle within the cardioid"-formula to avoid having to iterate some pixels, especially useful for extra speed with unzoomed high power Mandelbrots
   3. compiled with GCC: some formulas are faster, especially burning ship

Fixed problems:
   1. Mandelbrot power 2 julia sets with AVX was incorrect for pixels with iterationcount 0. The result was a weird pattern around Julia sets.
   2. Changing the gradient speed could suddenly shift the gradient by one color, as if the offset was changed. This is fixed by making the offset fractional (used to be integer), which is a quality improvement too. Old parameter files may be rendered slightly differently.

Known problems:
   1. Memory leak: about 5 MB of memory leaks for every 30 tabs openend and closed.

This will probably be the last version with new features until at least July 2022 because I'm very busy with other stuff. I wanted to add more features but I've tried to keep it simple to save time.
9
All rational numbers with at most two fractional decimals were characterized w.r.t. the quadratic Mandelbrot set using various exact and reliable methods (see below):

Code: [Select]
region analyzed [-2.00 .. +2.00] + i*[-2.00 .. 0]

80 601 total numbers
-----------------------------------------------
 7 591 interior to a hyperbolic component
     6 parabolic seeds
     2 Misiurewicz seeds
     2 hyperbolic centers
    12 neutral seeds (unclear of which type)
    52 uncharacterized (all pure real)

72 936 escaping

The image below shows the color-coded results (every 8x8 square pixel region represents one of the numbers of interest, the lower left being -2.00 - 2.00*i and increments of 0.01 to the right and to the top).
  • black, escaping
  • pale red, interior to a hyperbolic component
  • green, Misiurewicz
  • yellow, parabolic
  • white, neutral
  • cyan, hyperbolic center

The attached zip-archive contains text files for every bound seed, explaining the reasoning.

Methods
  • parabolic and neutral seeds were identified by symbolic manipulation of periodicity equations (using the computer-algebra system maxima), determining the periodic points, the multiplier and its argument, or symbolically solving the explicit equation for hyperbolic components of a certain period (linking the multiplier to the seed), after setting the derivative to +-1 and looking for rational solutions in the seed.
  • reliable computing algorithms:
    • exact orbit construction as long as the orbit remains a point interval to detect hyperbolic centers, Misiurewicz points and fast escaping.
    • interval orbit construction to detect escaping critical orbits.
    • guess/validation for interior seeds: an (uncontrolled) approximation of a periodic point was calculated with low precision, this region enlarged and subjected to reliable subdivision root finding to detect via the interval Newton operator periodic points of exact period p.
    • a series of number types was used, with precision 8200 . 2700 decimal digits sufficient in the end.[/l]
10
Image Threads / Re: Ducks/Kali
« Last post by pauldelbrot on Yesterday at 01:12:11 PM »
Kali Agate
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