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ufoace

Joined: 11 Mar 2013
Posts: 46

 Posted: Thu Jan 16, 2014 7:12 am    Post subject: i only have some icosahedron stars http://www.youtube.com/watch?v=_&feature=youtu.be and some icosahedron mutants: http://youtu.be/4Fv4pCuJVUk
inode

Joined: 27 Jan 2007
Posts: 127
Location: Austria

Posted: Sun Apr 27, 2014 8:23 am    Post subject: GridBall-Varations

Variations of an Algebraic Surface call 'GridBall', where you can change the integer value 'n'.

Will MathMod be able to create an animation e.g. with values 2,4,6,8,6,4 for 'n' ?
 Code: Name: PG_GridBallN6 /* Isosurface: PG_GridBallN6 4/2014 Gerd Platl */ F(): 0.0001 - ((x*x-y*y) * (y*y-z*z) * (z*z-x*x))^2 - 10*(x*x+y*y+z*z-1)^6 [x]: -1.11 , 1.11 [y]: -1.11 , 1.11 [z]: -1.11 , 1.11 ;
inode

Joined: 27 Jan 2007
Posts: 127
Location: Austria

Posted: Sun Apr 27, 2014 8:41 am    Post subject: Another variation...

This is - hard to believe - another variation of the Gridball.

Will MathMod be able to create an animation e.g. with values 2,4,6,8,6,4 for 'n' ?
 Code: Name: PG_RubberStar1 /* Isosurface: PG_RubberStar1 4/2014 Gerd Platl a variant of PG_GridBallN6 */ F(): 1 + 79*((x*x-y*y) * (y*y-z*z) * (z*z-x*x))^2 - (x*x+y*y+z*z-1)^6 [x]: -4 , 4 [y]: -4 , 4 [z]: -4 , 4 ;
nextstep

Joined: 06 Jan 2007
Posts: 539

Posted: Sun Apr 27, 2014 11:35 pm    Post subject:

Hi,
This is a good starting script to animate your gridball. You can define some variables if you need more calculation speed. The problem with your examples is that "n" is an integer but "t" in MathMod scripts is not a discrete variable.
 Quote: { "Iso3D": { "Component": [ "GridBall" ], "Fxyz": [ "0.0001-((x*x-y*y)*(y*y-z*z)*(z*z-x*x))^2-10*(x*x+y*y+z*z-1)^(23+int(20*sin(t*2*pi)))" ], "Name": [ "GridBall" ], "Xmax": [ "1.4" ], "Xmin": [ "-1.4" ], "Ymax": [ "1.4" ], "Ymin": [ "-1.4" ], "Zmax": [ "1.4" ], "Zmin": [ "-1.4" ] } }

_________________
Cheers,
Abderrahman
inode

Joined: 27 Jan 2007
Posts: 127
Location: Austria

Posted: Fri May 16, 2014 9:25 am    Post subject: PG_CagedStar1 = PG_GridBallN6 + PG_RubberStar1

RubberStar meets GridBall - together in harmonie...

 Code: Name: PG_CagedStar1 /* Isosurface: PG_CagedStar1  5/2014  Gerd Platl    = PG_GridBallN6 + PG_RubberStar1 */ F(): (4000 - ((x*x-y*y) * (y*y-z*z) * (z*z-x*x))^2 - 44*(x*x+y*y+z*z-16)^6)    * (1 + 89*((x*x-y*y) * (y*y-z*z) * (z*z-x*x))^2 -    (x*x+y*y+z*z-1)^6 ) [x]: -5 , 5 [y]: -5 , 5 [z]: -5 , 5 ;
inode

Joined: 27 Jan 2007
Posts: 127
Location: Austria

Posted: Fri May 16, 2014 12:41 pm    Post subject: Witch of Maria Agnesi

Todays Google theme is the 296. birthday of Versiera der Maria Agnesi...

 Code: Name: PG_WitchOfAgnesi X():tan(u) Y():cos(u)^2*cos(v) Z():cos(u)^2*sin(v) [u]:-1.3,  1.3 [v]:0,  2*pi
inode

Joined: 27 Jan 2007
Posts: 127
Location: Austria

Posted: Sat May 31, 2014 10:59 am    Post subject: A new world record ?

Hi all
Oliver Labs constructed 2004 a surface of degree 7 (septic) with 99 singularities - that's world record.
The maximum number of singularities are 104.

See http://www.algebraicsurface.net/
and http://imaginary.org/gallery/oliver-labs (and press >) for the comprehensive formula.

Martin Heider has published his new septic with more than 99 singularities.
Take a look at http://www.spektrum.com/artikel/950384&_z=798888
Is that a new world record ???

 Code: Name: MH_Septik2 /* Isosurface: MH_Septik2  Septik mit 105 ??? Singularitäten, Martin Heider  http://www.spektrum.com/artikel/950384&_z=798888 */ F():           (x*0.8358                        -(z-0.5)*0.549) * (x*cos( 2*pi/7)*0.8358 -y*sin( 2*pi/7)*0.8358 -(z-0.5)*0.549) * (x*cos( 4*pi/7)*0.8358 -y*sin( 4*pi/7)*0.8358 -(z-0.5)*0.549) * (x*cos( 6*pi/7)*0.8358 -y*sin( 6*pi/7)*0.8358 -(z-0.5)*0.549) * (x*cos( 8*pi/7)*0.8358 -y*sin( 8*pi/7)*0.8358 -(z-0.5)*0.549) * (x*cos(10*pi/7)*0.8358 -y*sin(10*pi/7)*0.8358 -(z-0.5)*0.549) * (x*cos(12*pi/7)*0.8358 -y*sin(12*pi/7)*0.8358 -(z-0.5)*0.549) - (x^2 +y^2 -4.731)^2 [x]: -4.5 , 4.5 [y]: -4.5 , 4.5 [z]: -4.5 , 8 ;
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