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Welcome to Fractal Forums > Fractal Math, Chaos Theory & Research > Mandelbrot & Julia Set > The 3D Mandelbulb > Theory > Choosing the squaring formula by location
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Author Topic: Choosing the squaring formula by location  (Read 28660 times)
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kram1032
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« Reply #60 on: June 02, 2013, 11:05:29 AM »
It's right above the picture in that same post, and it's kind of valid, but only if you're picky.
Quote from: msltoe on March 20, 2010, 03:26:47 AM
I conjecture that the real M3D, if it exists, requires minimal or no symmetrizing.
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KRAFTWERK
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« Reply #61 on: May 30, 2014, 11:46:23 AM »
Hello msltoe.

I just wanted to let you know that I managed to get a nice 3D print out of your beautiful formula.
Thank you for the formulas my friends!!!  A Beer Cup

I remember so well when I followed this thread and was blown away by that julia, this makes me extra happy now when I can wear it on my finger.



Klick the image for full view! Grin with closed eyes^
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msltoe
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« Reply #62 on: May 30, 2014, 03:09:50 PM »
Johan: Thanks for bringing this formula to life into a beautiful wearable ring.   
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KRAFTWERK
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« Reply #63 on: May 31, 2014, 09:41:07 PM »
Quote from: msltoe on May 30, 2014, 03:09:50 PM
Johan: Thanks for bringing this formula to life into a beautiful wearable ring.   

Oh, You have no idea how greatful I am for this approval Mike (?).
As I just said to jehovajah: this is the essance of this forum. I just love it, I love you all!  A Beer Cup afro
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M Benesi
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« Reply #64 on: May 31, 2014, 10:22:29 PM »
  That does look cool.  I bet a lot of us are thinking about building a CNC machine at some point- want to work with metal, wood, and stone instead of plastics. 
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DarkBeam
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« Reply #65 on: January 26, 2015, 12:31:00 PM »
Msltoe one day please share with us the tetrahedral variants smiley
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eiffie
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« Reply #66 on: January 27, 2015, 05:14:05 PM »
I am having fun revisiting these as DarkBeam digs them up. I made the formula continuous with some changes but the nice Julias are similar.
WebGL thingy: https://www.shadertoy.com/view/MtfGWM

If the glsl is confusing I could write it out plainly.

* msltoeJulia.jpg (33.45 KB, 530x318 - viewed 754 times.)
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DarkBeam
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« Reply #67 on: January 27, 2015, 05:36:08 PM »
Great idea I was looking for the continuous version!
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youhn
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« Reply #68 on: January 27, 2015, 05:58:41 PM »
Great stuff! Nice variety of shapes, which are even more beautiful when rotating and morphing. Those WebGL things are great.

I just dove into adding formulas to Mandelbulber v2, so yes please share the formula in the easy form:

newx = ...
newy = ...
newz = ...

This one is an addition to the ones already in MB3D?

MsltoeFoldQuat.m3f
MsltoeSym2.m3f
MsltoeSym3.m3f
MsltoeSym4.m3f
Msltoe_Sym.m3f

Can't check them all, since only Sym2, Sym3 and Sym4 have a description of the formula.

Sym2:
Code:
if abs(y) < abs(z) then exchange(y,z)
if y > z then x = -x
zr = 1 - z*z / (x*x + y*y + z*z)
x' = (x*x - y*y) * zr + Cx
y' = 2*x*y*zr * Y_multiplier + Cy
z' = 2*z * sqrt(x*x + y*y)

Sym3:
Code:
if abs(y) < abs(z) then exchange(y,z)
if y > z then {x = -x, z = -z}  
zr = 1 - z*z / (x*x + y*y + z*z)
x' = (x*x - y*y) * zr + Cx
y' = 2*x*y*zr * Y_multiplier + Cy
z' = 2*z * sqrt(x*x + y*y) + Cz

Sym4:
Code:
if abs(x) < abs(z) * XZ_sym-mul then exchange(x,z)
if abs(x) < abs(y) * XY_sym-mul then exchange(x,y)
if abs(y) < abs(z) * YZ_sym-mul then exchange(y,z)
if (x*z < 0) then z = -z;
if (x*y < 0) then y = -y;
x' = x*x - y*y - z*z + Cx
y' = 2*x*y + Cy
z' = 2*x*z + Cz
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eiffie
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« Reply #69 on: January 27, 2015, 06:17:59 PM »
This appears to be different since it is based on rotating yz into -pi/8.0, pi/8.0. What I changed was making this the absolute value so the edges of the "pie slice" align with the next slice. Then I don't rotate it back which may totally ruin the original idea but the julias around y=z=0 look similar.
Code:
float psi = fabs(fmod(atan2(z,y)+pi/8.0,pi/4.0)-pi/8.0);
float r=sqrt(y*y+z*z);
y=cos(psi)*r;
z=sin(psi)*r;
float m=1.0-z*z/(x*x+y*y+z*z);

newx=(x*x-y*y)*m; //also add the julia values here
newy=2.0*x*y*m;
newz=2.0*z*sqrt(x*x+y*y);
« Last Edit: January 27, 2015, 06:20:15 PM by eiffie » Logged
DarkBeam
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« Reply #70 on: January 27, 2015, 06:39:34 PM »
Mmm not sure. Cannot help.

Those were early formulas by Jesse. sad
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cKleinhuis
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« Reply #71 on: January 27, 2015, 10:55:49 PM »
awesome dudes, this one is really one that looks like one would expect

but errh, what do you mean by continuous version !? huh?
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DarkBeam
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« Reply #72 on: January 28, 2015, 12:01:44 AM »
Chris when a formula is discontinue the distance estimation fails ... you can't derive.
So continuous functions are always preferred angel
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cKleinhuis
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« Reply #73 on: January 28, 2015, 08:12:30 AM »
Quote from: DarkBeam on January 28, 2015, 12:01:44 AM
Chris when a formula is discontinue the distance estimation fails ... you can't derive.
So continuous functions are always preferred angel

i see, thank you wink undifferentiable functions are problemetatic, right sir smiley
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divide and conquer - iterate and rule - chaos is No random!
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