Alef
|
|
« on: December 10, 2012, 08:11:15 AM » |
|
Try swirlbrot by kram1032 and gravitational waves as discussed in buddhabrot thread. Simplest version is: z=(exp(flip(cabs(z)+atan2(z)) ) *z )^@power +c
It looks like rotated LKM's rotated mandelbrot, throught becouse of uneasy julia shapes you probably would want to use power 3 version instead of usual 2. No pics, too tired of buddhabrots;)
|
|
|
Logged
|
fractal catalisator
|
|
|
kram1032
|
|
« Reply #1 on: December 10, 2012, 09:29:11 AM » |
|
The generic idea would be to do: or: Where is a function of . In the most obvious case, you'd simply use and .
|
|
« Last Edit: December 11, 2012, 08:58:44 AM by kram1032 »
|
Logged
|
|
|
|
Alef
|
|
« Reply #2 on: December 11, 2012, 08:02:21 AM » |
|
Here it is. Mset with power 2 a julia set with power 2 and 3.
|
|
|
Logged
|
fractal catalisator
|
|
|
kram1032
|
|
« Reply #3 on: December 11, 2012, 09:01:36 AM » |
|
So the last one is power 3. What about the second Julia? Those are quite beautiful It's interesting to me to see that the swirl transform actually increases symmetry, somewhat stretching the three biggest bulb to at least apparently be the same size. Maybe, by animating the two frequencies ( and ), you could visualize how this symmetry comes about and, potentially, even find rotated versions of the original MSet if you just keep going...
|
|
« Last Edit: December 11, 2012, 09:08:46 AM by kram1032 »
|
Logged
|
|
|
|
Alef
|
|
« Reply #4 on: December 11, 2012, 01:47:02 PM » |
|
By animating would be too time consuming;) I was thinking about introducing this to Ultra Fractal and Chaos Pro database. All other m and j sets are of power 2. This one somewhat looks like rised in additional power 2. And it's very simmilar to LKM's rotated mandelbrot and alsou z=z^2+c; z=z*z/|z| , just that rotated mandelbrot realy aren't rotated, but this one is slightly rotated around coordinate start;) So there seems to be some good mathamatical background behind. It can't look simmilar just by accident. rotated-mandelbrot { ; Kerry Mitchell 06oct2002 ; ; Rotates the z variable in the standard Mandelbrot ; calculation each iteration. ; ; Use the 'rotation type' parameter to rotate before or ; after raising z to the desired power, or both before and ; after. The '+before, -after' setting rotates the opposite ; way after raising z to the power. ; ; The rotation angle is the 'rotation factor' times the angle ; of the pixel or z. The 'constant' setting in 'rotation type' ; makes the rotational angle a constant 'rotation factor' ; degrees. ; init: c=#pixel z=c+@manparam float t=0.0 float trad=@rotfac*#pi/180 rot=(0,0) loop: ; ; set up the rotation angle ; if(@angletype==1) ; pixel t=@rotfac*atan2(#pixel) elseif(@angletype==2) ; z t=@rotfac*atan2(z) else ; constant t=trad endif rot=cos(t)+flip(sin(t)) ; ; iterate z, taking into account the rotation type ; if(@rottype==1) ; before z=z*rot z=z^@power+c elseif(@rottype==2) ; after z=z^@power+c if(@angletype==2) t=@rotfac*atan2(z) rot=cos(t)+flip(sin(t)) endif z=z*rot elseif(@rottype==3) ; before & after z=z*rot z=z^@power+c if(@angletype==2) t=@rotfac*atan2(z) rot=cos(t)+flip(sin(t)) endif z=z*rot elseif(@rottype==4) ; +before, -after z=z*rot z=z^@power+c if(@angletype==2) t=@rotfac*atan2(z) rot=cos(t)+flip(sin(t)) endif z=z/rot else ; none z=z^@power+c endif bailout: |z|<@bailout default: title="Rotated Mandelbrot" periodicity=0 param manparam caption="perturbation" default=(0,0) endparam param power caption="power" default=(2,0) endparam float param bailout caption="bailout" default=1000.0 endparam param rottype caption="rotation type" default=1 enum="none" "before iterating" "after iterating" \ "before & after" "+before, -after" hint="How z is rotated each iteration." endparam float param rotfac caption="rotation factor" default=1.0 enabled=@rottype!="none" hint="If 'angle type' is 'constant', then this is the \ rotation angle in degrees. Otherwise, it is the factor \ that multiples the pixel or z angle to make the rotation \ angle." endparam param angletype caption="angle type" default=2 enum="constant" "pixel" "z" enabled=@rottype!="none" hint="Use 'constant' to specify a constant angle in degrees. \ Otherwise, the rotation is based on the angle of the pixel \ or the angle of z." endparam switch: type="rotated-julia" julparam=#pixel bailout=bailout power=power rottype=rottype rotfac=rotfac angletype=angletype }
|
|
« Last Edit: December 11, 2012, 02:08:31 PM by Alef »
|
Logged
|
fractal catalisator
|
|
|
simon.snake
Fractal Bachius
Posts: 640
Experienced Fractal eXtreme plugin crasher!
|
|
« Reply #5 on: December 11, 2012, 09:39:32 PM » |
|
Reminded me of one of my fractint formulas that produced this: Yours are great.
|
|
|
Logged
|
To anyone viewing my posts and finding missing/broken links to a website called www.needanother.co.uk, I still own the domain but recently cancelled my server (saving £30/month) so even though the domain address exists, it points nowhere. I hope to one day sort something out but for now - sorry!
|
|
|
kram1032
|
|
« Reply #6 on: December 11, 2012, 09:43:23 PM » |
|
neat. What formula does that?
|
|
|
Logged
|
|
|
|
simon.snake
Fractal Bachius
Posts: 640
Experienced Fractal eXtreme plugin crasher!
|
|
« Reply #7 on: December 11, 2012, 09:56:41 PM » |
|
simon0070-D { if (ismand) p = pixel z = pixel else p = p1 z = pixel endif z = (1/z)/(z*z): z = z * z + p |z| < 4 }
Parameters are as follows: Swirl { ; Fractint Version 2099 Patchlevel 8 reset=2099 type=formula formulafile=simon.frm formulaname=simon0070-D ismand=n passes=1 center-mag=-2.13163e-014/1.06581e-014/0.06643282/0.75 params=-1.7805108952668485/2.7597098893445381e-006 float=y maxiter=512 fillcolor=0 inside=0 periodicity=0 colors=0003be4no5zzzzz<3>zaXzVPuSL<3>_E5UA0PA2<3>56A05C1GM<3>5zzzzz<3>za\ XzVPuSL<3>_E5UA0PA2<3>56A05C1GM<3>5zzzzz<3>zaXzVPuSL<3>_E5UA0PA2<3>56A05\ C1GM<3>5zzzzz<3>zaXzVPuSL<3>_E5UA0PA2<3>56A05C1GM<3>5zzzzz<3>zaXzVPuSL<3\ >_E5UA0PA2<3>56A05C1GM<3>5zzzzz<3>zaXzVPuSL<3>_E5UA0PA2<3>56A05C1GM<3>5z\ zzzz<3>zaXzVPuSL<3>_E5UA0PA2<3>56A05C1GM<3>5zzzzz<3>zaXzVPuSL<3>_E5UA0PA\ 2<3>56A05C1GM<3>5zzzzz<3>zaXzVPuSL<3>_E5UA0PA2<3>56A05C1GM05C<3>4no5zzzz\ z<3>zaXzVPuSL<3>_E5UA0PA2<3>56A05C1GM<3>5zzzzz<3>zaXzVPuSL<3>_E5UA0PA2<4\ >05C1GM2SW }
|
|
|
Logged
|
To anyone viewing my posts and finding missing/broken links to a website called www.needanother.co.uk, I still own the domain but recently cancelled my server (saving £30/month) so even though the domain address exists, it points nowhere. I hope to one day sort something out but for now - sorry!
|
|
|
Alef
|
|
« Reply #8 on: December 13, 2012, 09:14:45 AM » |
|
Is this a z = (1/z)* 1/(z*z) ? Cos 1/(z/(z*z))= (z*z) /z= z
This works in interesting way: z=exp(flip( @frequency*cabs(z)+@spin*atan2(z)) ) *z z=z^2+c
UF operator flip switches real and imaginary parts, so it's like *i. In normal way: z=z*e^i(frequency*cabs(z)+spin*atan2(z))
Frequency is how mutch this is rotated around. Each 0.5 of spin works like additional power (simmetry), exept that it generates more stalked fractal. Probably it have something to do with radians. -2 spin and frequency =0 generates tricorn fractal.
Julias are especialy cool, like pictures on washing powders. I want this to upload to Ultra Fractal and Chaos Pro databases. What's your name to include in credits? Or should I put just "Variation by Kram1032"?
|
|
« Last Edit: December 13, 2012, 09:16:22 AM by Alef »
|
Logged
|
fractal catalisator
|
|
|
kram1032
|
|
« Reply #9 on: December 13, 2012, 11:54:02 AM » |
|
z = (1/z)/(z*z): z = z * z + p Huh... if I'm reading that right, it would do So essentially, it would do which, if I recall, does not yield what you have there... Alef, yeah, just go with kram1032, I guess Really nice stuff.
|
|
|
Logged
|
|
|
|
simon.snake
Fractal Bachius
Posts: 640
Experienced Fractal eXtreme plugin crasher!
|
|
« Reply #10 on: December 13, 2012, 07:38:45 PM » |
|
Probably my colour scheme has something to do with it, and if you look at the parameters, it shows that this is a julia (ismand=n).
Does that help?
|
|
|
Logged
|
To anyone viewing my posts and finding missing/broken links to a website called www.needanother.co.uk, I still own the domain but recently cancelled my server (saving £30/month) so even though the domain address exists, it points nowhere. I hope to one day sort something out but for now - sorry!
|
|
|
Ryan D
|
|
« Reply #11 on: December 14, 2012, 03:56:37 PM » |
|
z = (1/z)/(z*z): z = z * z + p Huh... if I'm reading that right, it would do So essentially, it would do which, if I recall, does not yield what you have there... In a Fractint formula, everything before the full colon (":") is an initial condition. Everything after the colon is iterated in the escape-time loop. So, the iteration loop executes only the z^2 + p portion. (Also, the final statement in a Fractint formula is the bailout condition.) Ryan
|
|
|
Logged
|
|
|
|
kram1032
|
|
« Reply #12 on: December 14, 2012, 07:30:29 PM » |
|
Ah, I see... The plane is initiated at and from there just iterated like the normal MSet. That makes sense. It's like those experiments where you'd do one thing up to iteration and after that iterate differently, in this case with .
|
|
« Last Edit: December 13, 2014, 12:15:03 AM by kram1032 »
|
Logged
|
|
|
|
TheRedshiftRider
|
|
« Reply #13 on: November 04, 2014, 07:05:43 PM » |
|
For images I make I mostly use a different program, but it has a similar way of making images like this. The whole function is different but the effects look allmost the same. This function is called mandelgrass.
|
|
|
Logged
|
Motivation is like a salt, once it has been dissolved it can react with things it comes into contact with to form something interesting.
|
|
|
|