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Author Topic: How to make a sphere?  (Read 4718 times)
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« on: January 29, 2016, 03:56:34 AM »

I am wondering if someone can post a formula of a spherical shaped fractal?

I don't want a fractal that has a sphere somewhere inside, but rather the whole fractal is a sphere.  If no one can post the param, could someone at least point me in the right direction as far as where to start?  What formula etc...?
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M Benesi
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« Reply #1 on: January 29, 2016, 05:36:51 AM »

A Julia of the default bulb with parameters (0,0,0) is a sphere, but it's not really that fractal...  

 You could use:

Code:
USE 1Bryan1's code below...

  To make something similar to the following (made with Fragmentarium... for the extra circular holes):
« Last Edit: January 30, 2016, 02:34:25 AM by M Benesi » Logged

1Bryan1
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« Reply #2 on: January 29, 2016, 09:22:44 AM »

A Julia of the default bulb with parameters (0,0,0) is a sphere, but it's not really that fractal... 
When I tried the parameters - formula 1 is blank.
Putting Formula 1 as "_BPolyhedronToSphere" seems to make any additional formula fall into a sphere.
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« Reply #3 on: January 29, 2016, 07:30:13 PM »

Ty both!  And yes by adding "_BPolyhedronToSphere", I was able to create that same image.
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1Bryan1
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« Reply #4 on: January 29, 2016, 10:13:49 PM »

For your info: if you put _Transform and _BPolyhedronToSphere as your first two formula then anything in Formula 3 (Fo 3) onwards AND tick "repeat from here" in Fo 3 - you can rotate, scale and move your spherical artwork within Formula 1.

For example, I have done this for M Benesi's parameter (below).
In the Navigator window - click on "Formula values:" to access the formula parameters and play with the values

Code:
Mandelbulb3Dv18{
g.....S....O/...w....2....U3sPmu.xn..rfXqZNVnF1EnsEfL/9SXzvfQW18m/amzyeFxQzzunxD
................................aNaNaNaNqz1........Y./..................y.2...wD
...Uz6....E2..../M.0/.....En....r/....E3......YwAh0F3cqD/..........m/dkpXm1....U
z.....kD12../2............................................U0.....y1...sD...../..
.z1...sDpMJWVRBRVxXL8xqB4IaKzWPaqn2ebkpDIp3yd8lxLwf3yw6vc3cMzsL0CyMx47qDaBVGFj/G
XxPaSbnvXJJKzKftxw2tFUpDU.....Y5..............sD.6....sD..G.....................
.............oAnAt1...sD....zw1.........................................A....k1.
.....CnAnz1.......kz.wzzz1.U..6.P....U5...EB....m....c3....F....6/...I1.....SF52
...U.qFG9yzb2zzzRYoWzz7lz16.pc..zXCc..kvrEtMc7xD6ocyFE0ujz1..........2.28.kFrA0.
.Ub96aAIVz9.1se7Umvxz0........../EU0.wzzz1...........s/...................E.2c..
zzzz.............0...................2./8.kzzzD............8....................
/EU0.wzzz1...................................2CcN/UvNPcveeWCNq0.yRiibHJJUk1f..XR
SvBmx3CcN/UvNPcvQsLsUa3.ibhVi1bTV1OK.sSq4uCly3CcN/UvNPcvMwLsUa3.ibhVinqTV1OK.sSq
4uCkz3CcN/UvNPcv..EsUa3feeWCNqGQIJ36wk8EwyLsUa3f................................
E....AU6V2E.....I....U....kLI7LMiBbNj7LP..................................E/3IU.
...................wz.......................................kL3k................
..............zD................................................................
.....................2.....3....0....wZEEx4PtVKNY7rPiFpPH/5OZ7LN...KIxqIkVKNmJ4.
............................../E........E.2........wz.........yD................
................................................................................
................................/....E/...k/....BJaPbJaQ7NoI....................
................4MU/....................6.2........wz.........zD........Uz1.....
................................................................................
............................................}
{Titel: main paras~}
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M Benesi
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« Reply #5 on: January 30, 2016, 01:18:36 AM »

When I tried the parameters - formula 1 is blank.
Putting Formula 1 as "_BPolyhedronToSphere" seems to make any additional formula fall into a sphere.
Thanks Bryan, formula 1 doesn't show up because the formula is called "_BPolyhedronlToSphere" (with an l in it!) on my computer.... probably should change it so this doesn't happen again.


  I originally called the formula "PolyhedralToSphere" and when I changed the name I left the l... apparently Andreas or Luca corrected my misspelling... and I didn't. 
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M Benesi
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« Reply #6 on: January 30, 2016, 01:21:49 AM »

Ohh- side note, mclarekin has been working on some of msltoe's old formulas, some of which have lots of spheres... might work for you.  
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mclarekin
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« Reply #7 on: January 30, 2016, 02:26:15 AM »

I am not quite sure what is needed???

 but the base shape of many fractals is a sphere, it is what you add afterwards that brings it away form being a sphere

and with the following code i can inflate a lot of fractals into a sphere

Quote
  double lengthTempZ = -z.Length();
  if (lengthTempZ > -1e-21) lengthTempZ = -1e-21;   //  z is neg.)
  z *= 1 + fractal->transformCommon.offset / lengthTempZ;
  z *= fractal->transformCommon.scale1;  // scale to control the size increase when using a positive radial offset
  aux.DE = aux.DE * fabs(fractal->transformCommon.scale1) + 1.0; // for analytic linear DE
  aux.r_dz *= fabs(fractal->transformCommon.scale1);
//  for analytic log  DE


* sphere.jpg (101.63 KB, 800x600 - viewed 448 times.)

* MB5 test qdsc1a 3200.jpg (130.91 KB, 600x600 - viewed 750 times.)
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Weber
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« Reply #8 on: January 30, 2016, 05:33:56 PM »

I too can get a basic sphere from a lot of formula combinations, but in this video at 5:20 is what I'm really trying to go for.  It probably wasn't made in M3D but I want to try and get as close as I can to recreating it.
This is my video, but those aren't my fractals.  I simply remixed them by adding music.

<a href="https://www.youtube.com/v/yrBXWVfxHoE&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/yrBXWVfxHoE&rel=1&fs=1&hd=1</a>.
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M Benesi
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« Reply #9 on: January 30, 2016, 07:01:04 PM »

The details look like an Amazing Box of some sort.  If you know the name of the original video, you might be able to ask someone the parameters.  


  At second glance, I'm thinking you could just do an Amazing Box with a bounding sphere (not sure of the name of a bounding sphere type formula for M3D??).

  You want to find a formula like:

  if (sqrt(pos.x^2+pos.y^2+pos.z^2) > bounding_sphere_radius) {x=max_bailout+1;}  
or
   DE= sqrt(pos.x^2+pos.y^2+pos.z^2) - bounding_sphere_radius;

  with pos being the 3 dimensional "pixel" location vector. 
« Last Edit: January 30, 2016, 07:12:37 PM by M Benesi » Logged

Aexion
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« Reply #10 on: January 31, 2016, 02:38:07 AM »

The details look like an Amazing Box of some sort.  If you know the name of the original video, you might be able to ask someone the parameters.  


  At second glance, I'm thinking you could just do an Amazing Box with a bounding sphere (not sure of the name of a bounding sphere type formula for M3D??).

  You want to find a formula like:

  if (sqrt(pos.x^2+pos.y^2+pos.z^2) > bounding_sphere_radius) {x=max_bailout+1;}  
or
   DE= sqrt(pos.x^2+pos.y^2+pos.z^2) - bounding_sphere_radius;

  with pos being the 3 dimensional "pixel" location vector. 
There's a third possibility:
The spherical version of the box, the one that iterates the radius as an extra dimension..
I think that I already have posted the formula..
Here's an example:


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M Benesi
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« Reply #11 on: January 31, 2016, 05:58:19 AM »

There's a third possibility:
The spherical version of the box, the one that iterates the radius as an extra dimension..
I think that I already have posted the formula..
  Which of the 30 Amazing box formulas is it?  cheesy
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Weber
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Just floating around


« Reply #12 on: January 31, 2016, 05:00:38 PM »

The details look like an Amazing Box of some sort.  If you know the name of the original video, you might be able to ask someone the parameters. 


  At second glance, I'm thinking you could just do an Amazing Box with a bounding sphere (not sure of the name of a bounding sphere type formula for M3D??).

  You want to find a formula like:

  if (sqrt(pos.x^2+pos.y^2+pos.z^2) > bounding_sphere_radius) {x=max_bailout+1;} 
or
   DE= sqrt(pos.x^2+pos.y^2+pos.z^2) - bounding_sphere_radius;

  with pos being the 3 dimensional "pixel" location vector. 
There's a third possibility:
The spherical version of the box, the one that iterates the radius as an extra dimension..
I think that I already have posted the formula..
Here's an example:
<Quoted Image Removed>



Well thanks both for your help!  I'll definitely be giving these a try.
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Aexion
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« Reply #13 on: February 01, 2016, 11:42:41 AM »

  Which of the 30 Amazing box formulas is it?  cheesy
30!! That's a  lot of variations to explore!!.. smiley
I just used the original one..

Here's the shader (I coded it in fragmentarium), not very good (I'm a little rusty in shader coding),but it works.
It basically takes the radius as an extra dimension.
Also, I have included the tetrahedron/octahedron one.. Its just the same as the sphere, but using
the dimensions in another way (quadray coordinates)..
If you add the extra dimension for the radius, you will get the sphere, but this time made of triangles.
Hope that helps..


* SphereBox.frag (2.25 KB - downloaded 146 times.)
* TetraBox2.frag (3.33 KB - downloaded 123 times.)
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« Reply #14 on: February 01, 2016, 05:01:49 PM »

So here's what I was able to achieve with the above mentioned formulas with a couple of my own added on.


* smoothsphere.jpg (80.28 KB, 800x392 - viewed 425 times.)
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