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Fractal Math, Chaos Theory & Research => Amazing Box, Amazing Surf and variations => Topic started by: Kali on June 01, 2011, 06:09:47 AM

Title: Kaliset + boxfold = Nice new 2D / 3D fractal
Post by: Kali on June 01, 2011, 06:09:47 AM

I just tried applying the positive part of Tglad's boxfold (from Mandelbox) to my formula Kaliset (2D), and the results are very interesting.

Not only Julias provides nices images with this, you can find nice shots inside the Mandelbrot version.

This is the code for the iteration:

Code:

x=abs(x)
y=abs(y)
if x>1
   x=2-x
endif
if y>1
   y=2-y
endif
m=x*x+y*y
x=x/m*scale+cx
y=y/m*scale+cy

Exponential smoothing for coloring, as always (but I'm trying new methods and variations for coloring, I'll make a post on this soon)

Some images...

This is the whole set for scale 1:

(http://img30.imageshack.us/img30/7008/kboxmand1.jpg)

This is the same with cx and cy values exchanged to reveal new patterns in flat zones, just like original Kaliset.

(http://img818.imageshack.us/img818/7567/kboxmand1rot.jpg)

This is scale 2 (also with cx and cy flip)

(http://img32.imageshack.us/img32/2157/kboxmand2rot.jpg)

And scale <1 works too. This is 0.5:

(http://img850.imageshack.us/img850/337/kboxmand05rot.jpg)

Some scenes from scale 1 Mandelbrot mode:

(http://img594.imageshack.us/img594/6537/kboxm11.jpg)

(http://img268.imageshack.us/img268/7206/kboxm12.jpg)

Scale 1 - Julia mode:

(http://img51.imageshack.us/img51/7673/kboxj12.jpg)

(http://img94.imageshack.us/img94/339/kboxj11.jpg)

Scale 2 - Mandelbrot mode:

(http://img861.imageshack.us/img861/5057/kboxm21.jpg)

(http://img37.imageshack.us/img37/1139/kboxm22.jpg)

Scale 2 - Julia mode:

(http://img202.imageshack.us/img202/8508/kboxj22.jpg)

(http://img560.imageshack.us/img560/5120/kboxj21.jpg)

The last one looks like 3D ;D

I'll post some more variations later. I'll try rotations and other stuff I have in mind.

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: Tglad on June 01, 2011, 08:26:41 AM

Superb images ;D
One to try would be sphere inverse, translate by some constant complex number, then flip around an arbitrary axis, then +c.
Because the only mandelbrots that have no stretch are those that don't swap handedness. (doesn't extend to 3d tho)

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: KRAFTWERK on June 01, 2011, 10:34:09 AM

I like the blue "X-ray" images Kali! :beer:

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: Kali on June 01, 2011, 03:27:27 PM

Quote

Superb images grin
One to try would be sphere inverse, translate by some constant complex number, then flip around an arbitrary axis, then +c.

Thanks Tom, and I'll try that later :dink:

Quote

I like the blue "X-ray" images Kali!

Haha, thanks... That image maps really look like x-ray ;D
Btw, I just made a huge image of flipped scale 3 whole mbrot map - I will upload and post the link later.

---

I've done two more images with smaller and higher scales.

This is 0.05 scale mbrot (used some crazy colors :)):

(http://img825.imageshack.us/img825/101/psychovi.jpg)

And a 10 scale julia:

(http://img171.imageshack.us/img171/3021/treebutterflyff.jpg)

I don't know about a 3D version, but what trafassel did with "Mandelbox variant 21" it's close to this... the differences are that I'm using abs function for extended patterns areas, and unrestricted sphere inverse instead of ballfold.

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: Kali on June 01, 2011, 08:33:40 PM

Well, I didn't get a non-streched mandelbrot mode, but adding a translation is nice for "tweaking" the Julias.

I did it this way: abs - boxfold - translation - inversion - addC (or second translation)

A couple of images I made with this:

(http://img685.imageshack.us/img685/9482/coveringlavaff.jpg)

(http://img835.imageshack.us/img835/3918/sparklesff.jpg)

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: yv3 on June 01, 2011, 09:15:05 PM

woha this formula is really nice, very much intresting places in it. Thank you for providing the iteration method, i will integrate it into my tool as "Kaliverse". But its without boxfold because my bad math knowledge. I added 4 "modifiers", here's the code :

Code:

	
	static double	x, y, m;
	static int		n;

	x=m_CustomRange2;
	y=m_CustomRange2;

	for(n=0; n<m_Iterations; n++)
	{
		x=abs(x);
		y=abs(y);

		if(x>m_CustomRange4) x=m_CustomRange3-x;
		if(y>m_CustomRange4) y=m_CustomRange3-y;

		m=x*x + y*y;

		x=x/m * m_CustomRange1 + m_StartX; 
		y=y/m * m_CustomRange1 + m_StartY; 

		if((x*x)+(y*y) > m_Magnitude )
		{
			m_C=int( float(n) * m_ColorPerIteration ); // Return color index from range 0 to (m_NumColors-1)
			return;
		}
	}

	m_C=0;

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: trafassel on June 01, 2011, 11:16:56 PM

Kali,
each time, when I think, that all possible types of fractals are examined, you publish some pictures like, in Reply#4. Thank you for sharing the pictures and formulas.

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: Kali on June 02, 2011, 01:12:48 AM

@yv3: Thanks for your comment... I'm don't have too much math knowledge either, but I'm always borrowing it from the guys here who really have some :)

"Boxfold" is what you just did:

Code:

if(x>m_CustomRange4) x=m_CustomRange3-x;
if(y>m_CustomRange4) y=m_CustomRange3-y;

But other values instead of >1 and 2- produces discontinuities, at least with the values I tried.

For best results, you would want to use an inner coloring, instead of escapetime.
To implement exponential smoothing, do this:

Declare this variables (double): sum, mold
Then replace this code:

Code:

if((x*x)+(y*y) > m_Magnitude )
		{
			m_C=int( float(n) * m_ColorPerIteration ); // Return color index from range 0 to (m_NumColors-1)
			return;
		}

with this:

Code:

sum+=Math.Exp(-1/Math.Abs(mold-m))
mold=m

Then use the result of the variable sum after all the iterations as a color index. I suggest multiplying by a "color density" factor and then map the results to m_NumColors with "mod" function (I don't remember how it's implemented in C, but I think is with symbol %)

It should be like this, but I'm not sure:

Code:

m_C=int(sum*m_colordensity) % m_NumColors

---

@trafassel: You are welcome, thanks. I don't know if "Kaliset" and the derived formulas like this are such a novelty or really a great finding, but I'm glad you like it and I really appreciate your words...
Remember that "the possibilities are infinite", so I guess there is still a lot of things to discover :dink:

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: yv3 on June 02, 2011, 12:13:32 PM

@Kali:
I always thought that the exponential smoothing does not work on fixed palettes. Thank you very much! It looks beautiful!

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: matsoljare on June 02, 2011, 07:44:57 PM

Don't forget trying to vary the other parameters by the axis, as well....

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: KRAFTWERK on June 03, 2011, 11:34:54 AM

I love the "electric triangle" and the other image too in your last post Kali! :beer:

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: dwsel on July 01, 2011, 04:44:19 PM

Recently I've been implementing various formulas of yours using good old Tierazon with its tiny formula parser. And then I came to the boxfold part:

Code:

if x>1
   x=2-x
endif

which literately says for me:

Code:

if (x>1)
   x=2-x;
else
   x=x;

It looks like boxfold can be calculated without if clause, just like:

Code:

-abs(x-1)+1;

Won't dropping 'if' in favour of 'abs' speed up calculations?

I'll see if it's a good path and post some images if I get kaliset + boxfold implemented in this way.
Have a nice day!

dwsel

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: Kali on July 01, 2011, 08:17:49 PM

Quote from: dwsel on July 01, 2011, 04:44:19 PM

Recently I've been implementing various formulas of yours using good old Tierazon with its tiny formula parser. And then I came to the boxfold part:

Code:

if x>1
   x=2-x
endif

which literately says for me:

Code:

if (x>1)
   x=2-x;
else
   x=x;

It looks like boxfold can be calculated without if clause, just like:

Code:

-abs(x-1)+1;

Won't dropping 'if' in favour of 'abs' speed up calculations?

I'll see if it's a good path and post some images if I get kaliset + boxfold implemented in this way.
Have a nice day!

dwsel

Well, I think it's a more elegant way to do it, but I'm not sure about performance improvement. If condition x>1 is false, no further operations are needed, x remains the same. but using your method, I count 4 math operations and a variable asignment performed on every iteration. Even when I don't know exactly how expensive is an "if" statement compared to abs, sum and change of signs, I think it should be at least the same. Anyway it's a good observation you made.

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: DarkBeam on July 01, 2011, 09:00:37 PM

I have coded a version of this fractal for mandelbulb but looks different. Tomorrow look again :)

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: Kali on July 01, 2011, 09:13:54 PM

Quote from: DarkBeam on July 01, 2011, 09:00:37 PM

I have coded a version of this fractal for mandelbulb but looks different. Tomorrow look again :)

:now:

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: dwsel on July 01, 2011, 09:57:16 PM

Quote from: Kali on June 02, 2011, 01:12:48 AM

@yv3: Thanks for your comment... I'm don't have too much math knowledge either, but I'm always borrowing it from the guys here who really have some :)

"Boxfold" is what you just did:

Code:

if(x>m_CustomRange4) x=m_CustomRange3-x;
if(y>m_CustomRange4) y=m_CustomRange3-y;

But other values instead of >1 and 2- produces discontinuities, at least with the values I tried.

If you plot a graph of this function and substitute with values other than 1 and 2- it's very likely that you'll not choose 'correct' values and you get discontinuity, but... if you try my method instead and treat formula with:
1. absolute value
2. translation
3. mirror by x axis (f(x) = -x)
4. repeat 1-3 how many times you like for multiple folds ;)
then you should never get discontinuity. On the other side note that function won't be differentiable, what might be important for calculating 3d Mandel (I don't know math standing behind it).

I'm waiting for your results :joy:

P.S. Sorry for my mathematical english - it's pretty bad. Please point out when I write something unclear or unintentionally exchange math terms.
P.P.S. I'll try to implement thing in ChaosPro instead of Tierazon. Just imagine these slowly rendering, kilometre long formulas where abs(x) is for example calculated as ((real(z)^2)^0.5) :D

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: dwsel on July 02, 2011, 01:02:45 AM

Img 1

Code:

-abs(x-1.5)+1.5;

Img 2

Code:

-abs(x-1.25)+1.25;

Img 3

Code:

if (x>1.8)
   x=2-x;
else
   x=x;

Img 4. From lightest to darkest green, plot of functions used in Img 1, Img 2, -abs(x-1)+1, and in Img 3 (shows discontinuity at 1.8 )

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: Kali on July 02, 2011, 02:24:06 AM

Now I see it clearer, dwsel. It's very good, indeed. I just realized also that I did something like that in this "mandelbrot-tricorn-combo" image some days ago:

(http://img14.imageshack.us/img14/434/mandeltricorn.jpg)

I used abs and translations, but I was stupid enough to not realizing it's similar to a "boxfold" :embarrass:

I will try more things later using your idea.

Thanks!

P.S.:Good renders! and your english is better than mine, for sure!

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: Kali on July 02, 2011, 07:39:45 AM

This is complex-number kaliset using this formula, based on dwsel's suggestion: z=1/(abs(z+t)-t)+c

t=(1.00,1.00)

(http://img196.imageshack.us/img196/6739/dwselfoldkaliset1.jpg)

t=(0.75,0.25)

(http://img28.imageshack.us/img28/2753/dwselfoldkaliset2.jpg)

t=(5.00,1.00)

(http://img833.imageshack.us/img833/3466/dwselfoldkaliset3.jpg)

And a Julia I picked from the last one:

(http://img35.imageshack.us/img35/8467/dwselfoldkaliset4.jpg)

@dwsel: One thing I forgot to mention, is that "full" boxfold is, i.e. for x axis:

Code:

if x>1 
  x=2-x
elseif x<1
  x=-2-x
endif

I tried to do the same with nested abs's but I couldn't, maybe you can find the way to do it?

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: Kali on July 02, 2011, 08:24:23 AM

An intrincate pattern of trees:

(http://img194.imageshack.us/img194/9994/dwselfoldkalisetc.jpg)

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: Syntopia on July 02, 2011, 09:37:05 AM

Quote from: Kali on July 02, 2011, 07:39:45 AM

@dwsel: One thing I forgot to mention, is that "full" boxfold is, i.e. for x axis:

Code:

if x>1 
  x=2-x
elseif x<1
  x=-2-x
endif

I tried to do the same with nested abs's but I couldn't, maybe you can find the way to do it?

You should take a look at Rrrola's clever Mandelbox implementation in Boxplorer:

Code:

    // box folding: if (p>1) p = 2-p; else if (p<-1) p = -2-p;
    //    p.xyz = abs(1.0+p.xyz) - p.xyz - abs(1.0-p.xyz);  // add;add;abs.add;abs.add (130.4%)
    //    p.xyz = clamp(p.xyz*0.5+0.5, 0.0, 1.0) * 4.0 - 2.0 - p.xyz;  // mad.sat;mad;add (102.3%)
    p.xyz = clamp(p.xyz, -1.0, 1.0) * 2.0 - p.xyz;  // min;max;mad

    // sphere folding: if (r2 < minRad2) p /= minRad2; else if (r2 < 1.0) p /= r2;
    float r2 = dot(p.xyz, p.xyz);
    p *= clamp(max(minRad2/r2, minRad2), 0.0, 1.0);  // dp3,div,max.sat,mul

Using a clamp-operator is 30% faster (on a GPU), but if you haven't got one, there is still the 'abs' version in line 2.

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: DarkBeam on July 02, 2011, 11:12:17 AM

Quote from: Kali on July 02, 2011, 07:39:45 AM

Code:

if x>1 
  x=2-x
elseif x<1
  x=-2-x
endif

I tried to do the same with nested abs's but I couldn't, maybe you can find the way to do it?

dwsel meant fold-abs(+fold-abs(x)) (else, you are losing your 1st abs! :evil1: )
If you simply read Jesse's formulas you will find the abs version of folding;

x = abs(x+Fold) - abs(x-Fold) - x

:tease: ;D :dink: :dink:

Anyway, if I do a unrestricted sphere inversion I don't see anything good in Mandelbulb :sad1:

A good compromise is to make normal conditional inversions. Anyway "my" fractal still looks very different from yours, I really don't know why :( there is no possible sign error!

(http://img38.imagefra.me/i572/kriptokapi/eba_2c0_u6bci.jpg) (http://i.imagefra.me/c38ied5f)

EDIT. I remember this happened for other fractal formulas too. :) Maybe Jesse uses "windows screen axis orientation", rather than the "mathematical correct" one - this should explain everything. Well well! ::) ::)

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: Kali on July 02, 2011, 01:57:33 PM

@Syntopia: I will try that, thanks!

@Luca:

Quote from: DarkBeam on July 02, 2011, 11:12:17 AM

dwsel meant fold-abs(+fold-abs(x)) (else, you are losing your 1st abs! :evil1: )
If you simply read Jesse's formulas you will find the abs version of folding;

About dwsel suggestion, sorry but I don't see where she's using two abs like that :hmh:

Thanks for the solution, and yeah, I know I should read more other people's work, but I like to figure out things by myself when I can. I tried but I was tired last night so I stopped (my mathematical mind was already sleeping :D). Anyway I was doing some interesting things with just abs(z+t)-t

About the 3D version you made, is not bad at all, what about the Julias?

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: Kali on July 02, 2011, 04:37:23 PM

Currently playing with asymmetrical folding

z=1/(abs(z+0.25+0.50i)-abs(z-0.50-1.00i)-z)-1.50-1.50i = Full moon ;D

(http://img9.imageshack.us/img9/1776/fractalmoonsff.jpg)

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: dwsel on July 02, 2011, 05:16:33 PM

Quote from: DarkBeam on July 02, 2011, 11:12:17 AM

dwsel meant fold-abs(+fold-abs(x)) (else, you are losing your 1st abs! :evil1: )
If you simply read Jesse's formulas you will find the abs version of folding;
x = abs(x+Fold) - abs(x-Fold) - x

I've suggested sth like:
-abs(-abs(-abs(x-a)+b)-c)+d) and so on...
i.e. abs(-abs(x-1.5)+1.5)-0.2 - light green function
or -abs(-abs(x-0.5)+1.25)-0.75 - dark green

and so far haven't worked out a rule where to use + and - :P
I think that if you use - abs then you should use + parameter and accordingly

[don't know which edit it is :D]
I know already - before applying abs() function have to cross x axis :)

Articles http://home.windstream.net/okrebs/page43.html (http://home.windstream.net/okrebs/page43.html) and http://www.abac.edu/gclement/MATH1111/Resources/Symmetry.pdf (http://www.abac.edu/gclement/MATH1111/Resources/Symmetry.pdf) are reflecting roughly what I base my reaserch on.

Quote from: Syntopia on July 02, 2011, 09:37:05 AM

You should take a look at Rrrola's clever Mandelbox implementation in Boxplorer:

Code:

    // box folding: if (p>1) p = 2-p; else if (p<-1) p = -2-p;
    //    p.xyz = abs(1.0+p.xyz) - p.xyz - abs(1.0-p.xyz);  // add;add;abs.add;abs.add (130.4%)
    //    p.xyz = clamp(p.xyz*0.5+0.5, 0.0, 1.0) * 4.0 - 2.0 - p.xyz;  // mad.sat;mad;add (102.3%)
    p.xyz = clamp(p.xyz, -1.0, 1.0) * 2.0 - p.xyz;  // min;max;mad

    // sphere folding: if (r2 < minRad2) p /= minRad2; else if (r2 < 1.0) p /= r2;
    float r2 = dot(p.xyz, p.xyz);
    p *= clamp(max(minRad2/r2, minRad2), 0.0, 1.0);  // dp3,div,max.sat,mul

then full boxfold is as far as I understand (red function):

Code:

if (p>1)
  p = 2-p;
else if (p<-1)
  p = -2-p;

Blue function is something as ugly as (I hope it can be simplified):
(abs((x/2-0,5)-(2*floor(x/4-0,25))-1)-0,5)*2
and have even infinite number of folds

Each of functions using abs (green ones) has odd number of folds while original boxfold has only 2 folds as well as (0,0) symmetry which I don't know how to achieve here.

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: DarkBeam on July 02, 2011, 05:39:58 PM

;D

I am uploading this formula version

Scale = Scale + Scale_vary*(abs(Scale)-1)
x = Fold-abs(abs(x+FoldXM)-Fold)-FoldXM
y = Fold-abs(abs(y+FoldYM)-Fold)-FoldYM
z = Fold-abs(abs(z+FoldZM)-Fold)-FoldZM
rr = pow(x*x + y*y + z*z + w*w, R_power)
if rr < sqr(Min_R) then m = Scale/sqr(Min_R) else
if rr < 1 then m = Scale/rr else m = Scale
x = x * m + Cy
y = y * m + Cx
z = z * m + Cz

Gives lots of interesting julias, so much to explore. :)

The "unconditional" formula is troubleful, as many other Kali works... ;D For now take a look at it. Going to upload it then post some "photos" ;D herrrre

Title: some shots!!!
Post by: DarkBeam on July 02, 2011, 06:00:15 PM

I like to choose with the point and click the seeds! See some random spots, they are already stunning as they are...

(http://img37.imagefra.me/i572/kriptokapi/iyhk_6ba_u6bci.jpg) (http://i.imagefra.me/8b8iedoa)

:verysurprised: :verysurprised: :verysurprised:

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: Kali on July 02, 2011, 06:28:36 PM

@dwsel: I'm definitely going to try that foldings later, will post some images but maybe I will open a new thread because this one was hijacked by Darkbeam and his boring 3D stuff ;D
I was trying first the full boxfold using weird values, I like how it works and the less symmetric images... see this one (http://www.fractalforums.com/index.php?action=gallery;sa=view;id=7741)

Quote from: DarkBeam on July 02, 2011, 05:39:58 PM

The "unconditional" formula is troubleful, as many other Kali works... ;D For now take a look at it. Going to upload it then post some "photos" ;D herrrre

Yeah, troubleful for 3D, but anyway nobody are interested in 3D fractals lately ;D
The main problem with my all-inside formulas in 3D is that they are designed for 4D beings who have real 3D vision, not 2D stereo like we humans :D

Besides the jokes, your images look very interesting!

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: DarkBeam on July 02, 2011, 06:48:59 PM

Heh thanks... :dink:

for dwsel. can you make me a graphic of this function?

(when x1=x-2*round(x/2); round(0.49999)=0 and round(0.5)=1 )
y=abs(x1+1) - abs(x1-1) - x1

In assembly I don't have floor() and ceil() functions, only it, but I can easily combine functions to get complex results :)

the graphic of y should be the infinite folding

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: DarkBeam on July 02, 2011, 07:01:25 PM

Quote from: DarkBeam on July 02, 2011, 06:48:59 PM

Heh thanks... :dink:

for dwsel. can you make me a graphic of this function?

(when x1=x-4*round(x/4); round(0.49999)=0 and round(0.5)=1 )
y=abs(x1+1) - abs(x1-1) - x1

In assembly I don't have floor() and ceil() functions, only it, but I can easily combine functions to get complex results :)

the graphic of y should be the infinite folding

Corrected; this is the correct one! :) I will do some functions with it soon ^-^

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: dwsel on July 03, 2011, 12:02:08 AM

Quote from: DarkBeam on July 02, 2011, 07:01:25 PM

Quote from: DarkBeam on July 02, 2011, 06:48:59 PM

Corrected; this is the correct one! :) I will do some functions with it soon ^-^

y is light gray
BTW. Just in case ;) I plot functions in Excel at the moment, Libre Office Calc does the same job as well, but for more 'serious plotting' I suggest Scilab http://www.scilab.org/

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: dwsel on July 03, 2011, 01:15:16 AM

It's not that big surprise that 2D is very noisy even at low number of iterations (10). Here's mandel view and one of the julias (second did not fit into attachment) - viewed from distance are quite regular - they look like a carpet then ;)

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: DarkBeam on July 03, 2011, 10:18:21 AM

:-* thanks, released Infy folding now.

I made too a xl graph. :dink:

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: Kali on July 04, 2011, 04:20:37 AM

I just uploaded this to the gallery. Is my simplified version of KIFS (or genIFS), but I used custom transforms to implement a folding based on dwsel suggestions.

(http://nocache-nocookies.digitalgott.com/gallery/7/thumb_3869_04_07_11_4_08_48.jpeg)

http://www.fractalforums.com/index.php?action=gallery;sa=view;id=7757

Title: Re: Kaliset + boxfold = Nice new 2D fractal
Post by: Kali on July 05, 2011, 03:32:30 PM

I tried the iterated folding idea, prior to the inversion, this way (UF5 code):

while l<n
l=l+1
z=-abs(z-t)+t
z=-real(z)+imag(z)*1i
t=t*f
endwhile

n=number of loops
t=folding "translation" (complex)
f=subsequent folds scaling

In the following image, the fold iterations are 5, with (1,1) translation and 0.5 folding scale

(http://img197.imageshack.us/img197/1275/foldloop.jpg) (http://img197.imageshack.us/i/foldloop.jpg/)