Parplot Presets

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A list of some of the preset shapes that Parplot variation produces. There’s more now, but this should give you a flavour of what to expect.

A list of Parplot presets by Don Town, Image samples 1-37 by Sarah Griffin.

ABOUT THIS INDEX
Each image in this table is a single JWildfire layer using several transforms. Front, back and side views were prepared by working in the different planes of XY, YZ, and ZX. Some figures are labeled for different color modes as well. Orange numbering was applied with Irfanview. Credits and sourcing are given wherever possible.
Preset IDPresetExample ImageCreatorNotes
03D lissajousSG Parplot Sample 00Andreas Maschkex=cos(u)*(4+cos(v))
y=sin(u)*(4+cos(v))
z=4*sin(2*u)+sin(v)*(1.2-sin(v))
umin = 0.0, umax = 2 * pi
vmin = 0.0, vmax = 2 * pi
1coneSG Parplot Sample 01Andreas Maschkecolor_modes 0-3
x=cos(v)*sin(2*u)
y=sin(v)*sin(2*u)
z=sin(2*v)*sqr((cos(u)))
umin = 0.0, umax = pi
vmin = 0.0. vmax = pi
2shellSG Parplot Sample 02 Andreas Maschkecolor_mode=2; the center line is from the gradient.
x=cos(u)*(exp(u/10)-1)*(cos(v)+0.8)
y=sin(u)*(exp(u/10)-1)*(cos(v)+0.8)
zformula=exp(u/10)-1)*sin(v)
umin = 0.0, umax = 5 * pi
vmin = 0.0, vmax = 2 * pi
3torusSG Parplot Sample 03Andreas Maschkexformula = cos(v)*(2+sin(u+v/3))
yformula = sin(v)*(2+sin(u+v/3))
zformula = cos(u+v/3)
umin = 0.0, umax = 2 * pi
vmin = 0.0, vmax = 2 * pi
4helixSG Parplot Sample 04Andreas Maschkecolor_mode set as indicated
xformula = cos(u)*(2+cos(v))
yformula = sin(u)*(2+cos(v))
zformula = (u-2*pi)+sin(v)
umin = 0.0; umax = 4.0 * pi
vmin = 0.0, vmax = 2.0 * pi
5wavy discSG Parplot Sample 05Andreas Maschkex = u*cos(v)
y = u*sin(v)
z = sqr(cos(4.0*u))*exp(0-u)
umin = 0.0, umax = pi
vmin = 0.0, vmax = 2.0 * pi
6klein bottleSG Parplot Sample 06Andreas Maschkex = x=cos(u)*(2.0+sqr(cos(u/2.0))*sin(v))
y = sin(u)*(2.0+sqr(cos(u/2.0))*sin(v))
z = sqr(cos(u/2.0))*cos(v)
umin = 0.0 – pi, umax = pi
vmin = 0.0 – pi, vmax = 2.0 * pi
7Case 7SG Parplot Sample 07Andreas Maschkex = cos(u)*(4+cos(v))
y = sin(u)*(4+cos(v))
z = 3*sin(u)+(sin(3*v)*(1.2+sin(3*v)))
umin = 0.0, umax = 2.0 * pi
vmin = 0.0, vmax = 2.0 * pi
8Case 9SG Parplot Sample 08Andreas Maschkex= = u*cos(v)
y = v*cos(u)
z = u*v*sin(u)*sin(v)
umin = 0.0 – pi, umax = pi
vmin = 0.0 – pi, vmax = pi
9Hershey KissSG Parplot Sample 09Andreas Maschkex = cos(u)*sin(v*v*v/(pi*pi))
y = sin(u)*sin(v)
z = cos(v)
umin = 0.0, umax = 2.0 * pi
vmin = 0.0, vmax = pi
10Case 10SG Parplot Sample 010Andreas Maschkex`= cos(u)*((cos(3*u)+2)*sin(v)+0.5)
y` = sin(u)*((cos(3*u)+2)*sin(v)+0.5)
z` = (cos(3*u)+2)*cos(v)
umin = 0.0, umax = 2.0 * pi
vmin = 0.0, vmax=2.0 * pi
11Varigated sphereSG Parplot Sample 011Andreas Maschkesolid render
source:https://reference.wolfram.com/language/tutorial/Paramet
ricPlots.html
x= sin(u)*sin(v)+0.05*cos(20*v)
y = cos(u)*sin(v)+0.05*cos(20*u)
z = cos(v)
umin = -pi, umax = pi
vmin = -pi, vmax = pi
12ShellSG Parplot Sample 012Dimitri Augusto Rochahttps://renklisheyler.wordpress.com/2012/04/27/algebraicsurfaces/

x=2.0*(1.0-exp(u/(6.0*pi)))*cos(u)*sqr(cos(v/2.0))
y = 2.0*(-1.0+exp(u/(6.0*pi)))*sin(u)*sqr(cos(v/2.0))
z =1.0-exp(u/(3.0*pi))-sin(v)+exp(u/(6.0*pi))*sin(v)
umin = 0,umax = 6 * pi
vmin = 0, vmax = 2* pi
13SlinkySG Parplot Sample 013Don Townhttp://mathworld.wolfram.com/Slinky.html

color_modes 0-3
x=(6+2*cos(u*v))*cos(u) ---- R=6, a=2, h=2
y=(6+2*cos(u*v))*sin(u)
z=(2*u+2*sin(u*v))
umin= 0.0, umax= 6 * pi
vmin= 0.0, vmax= 6 * pi
14Real slinkySG Parplot Sample 014Frank Baumannx=(1.0+0.25*cos(75.0*u))*cos(u)
y=(1.0+0.25*cos(75.0*u))*sin(u)
z=u+sin(75.0*u)
umin= -2 * pi, umax= 2 * pi
vmin= -2 * pi, vmax= 2 * pi
15Spherical spiralSG Parplot Sample 015Frank Baumannx= 7.83*cos((v-pi)/2)*(cos(16.4*v))
y= 7.83*cos((v-pi)/2)*(sin(16.4*v))
z= 7.83*sin((v-pi)/2)
umin= 0.0, umax= 2 * pi
vmin= 0.0. vmax= 2 * pi
16Spherical roseSG Parplot Sample 016Frank Baumannxformula= (2 + sin(7*u + 5*v))*cos(u)*sin(v)
y= (2 + sin(7*u + 5*v))*sin(u)*sin(v)
z= (2 + sin(7*u + 5*v))*cos(v)
umin= -pi, umax= pi
vmin= -pi, vmax= pi
17Folded boxSG Parplot Sample 017 1Frank BaumannPreset_id=17
x= sin(u)*sin(v)
y= cos(v)*cos(u)
z= sin(sin(u)+cos(v))
umin= -pi, umax= pi
vmin= -pi, vmax= pi
18Wavy heartSG Parplot Sample 018Frank Baumannx= (2*v*cos(u))
y= 2.0*v*(sin(u))+v*fabs(cos(u))
z= cos(3*v)*sin(3*v)2
umin= 0.0, umax= 63
vmin= 0.0, vmax= 6
1Turn your heart right side up with the Affine transform-Vertical flip
button in the XY plane.
2Change the amplitude of waves by changing zformula value as
seen in this equation: a*cos(f*v)*a*sin(f*v) Change the frequency
of waves by changing value f. a=amplitude; f=frequency.
3To remove the pierced look, set umin to below -0.3.
19Interesting ShapeSG Parplot Sample 019Frank Baumanncolor_modes 0-3
x=v*sin(fabs(u))
y= u*sin(fabs(v))
z= u+fabs(sin(v*u))
umin= -pi, umax= pi
vmin= -pi, vmax= pi
20Bubble GumSG Parplot Sample 020Frank Baumannxformula= cos(u)*(6-(5/4+sin(3-v))*sin(v-3-u))
y= (6-(5/4+sin(3*v))*sin(v-3*u))*sin(u)
z= -cos(v-3*u)*(5/4+sin(3*v))
umin= -pi, umax= pi
vmin= -pi, vmax= pi
21Twisted TorusSG Parplot Sample 021Frank Baumannxformula= (4+(sin(4*(v+2*u))+1.25)*cos(v))*cos(u)
y= (4+(sin(4*(v+2*u))+1.25)*cos(v))*sin(u)
z= ((sin(4*(v+2*u))+1.25)*sin(v))
umin= -pi, umax= pi
vmin= -pi, vmax= pi
22VaseSG Parplot Sample 022Frank Baumannxformula= u
y= sin(v)*(u*u*u+2.0*u*u-2.0*u+2.0)/5.0
z= cos(v)*(u*u*u+2.0*u*u-2.0*u+2.0)/5.0
umin= -2.3, umax= 1.3
vmin= 0.0, vmax= 2 * pi
23BreatherSG Parplot Sample 023Frank Baumanncolor_modes 0-3
xformula=-0.8*u+(2*0.75*cosh(0.5*u)*sinh(0.5*u))/
(0.5*((sqrt(0.75)*sqr(cosh(0.5*u)))
+sqr(0.5*sin(sqrt(0.75)*v))))
y=(2.0*sqrt(0.75)*cosh(0.5*u)*(-
(sqrt(0.75)*cos(v)*cos(sqrt(0.75)*v))-
sin(v)*sin(sqrt(0.75)*v)))/(0.5*sqr((sqrt(0.75)*cosh(0.5*u))
+sqr(0.5*sin(sqrt(0.75)*v))))
z=(2.0*sqrt(0.75)*cosh(0.5*u)*((sqrt(0.75)*sin(v)*cos(sqrt
(0.75)*v))+cos(v)*sin(sqrt(0.75)*v)))/(0.5*sqr((sqrt(0.75)*
cosh(0.5*u)) +sqr(0.5*sin(sqrt(0.75)*v))))
umin= -15, umax= 15
vmin= -24.55, vmax= 22
1 This one can be slow to render, depending on your computer's
capabilities)
24LissajousSG Parplot Sample 024Frank Baumannx= cos(1*u+0)+0.06*sin(1*v) --- Change the 0 value for phase
shift and the u multiplier for frequency
y= cos(15*u+0)-0.6*cos(1*v) --- Change the 0 value for phase
shift and the u multiplier for frequency
z= sin(12*u+0)+0.06*sin(1*v) --- Change the 0 value for phase
shift and the u multiplier for frequency
umin= 0.0, umax= 2 * pi
vmin= -0.5, vmax= 0.5
1 These figures are as written, with no changes to constants (0
values) or coefficients (u multipliers).
25Double mushroomSG Parplot Sample 025Frank Baumann(set pitch close to 90 degrees to see mushroom)
x= (cos(2*u))/(sqrt(2)+sin(2*v))
y= sin(2*u)/(sqrt(2)+sin(2*v))
z= v/(sqrt(5)+cos(2*v))
umin= -pi, umax= pi
vmin= -3, vmax= 8
26Triangluoid trefoilSG Parplot Sample 026Frank Baumanncolor_modes 0-3
x= 2*sin(3*u)/(2+cos(v))
y= 2*(sin(u)+2*sin(2*u))/(2+cos(v+2*pi/3))
z= (cos(u)-2*cos(2*u))*(2+cos(v))*(2+cos(v+2*pi/3))/4
umin= -pi, umax= pi
vmin= -pi, vmax= pi
27Shell#1SG Parplot Sample 027Frank Baumanncolor_modes 0-3
x= pow(1.2,u)*(1+cos(v))*cos(u)
y= pow(1.2,u)*(1+cos(v))*sin(u)
z= pow(1.2,u)*sin(v)-1.5*pow(1.2,u)
umin= -12, umax= 6
vmin= -pi, vmax= pi
28Shell#2SG Parplot Sample 028Frank Baumanncolor_modes 0-3
x= u*cos(u)*(cos(v)+1)
y= u*sin(u)*(cos(v)+1)
z= u*sin(v)-((u+3)/8*pi)*u/3
umin= 0.0, umax= 20
vmin= -pi, vmax= pi
29Trefoil knotSG Parplot Sample 029Frank Baumannx= cos(u)*cos(v)+3*cos(u)*(1.5+sin(u*5/3)/2)
y= sin(u)*cos(v)+3*sin(u)*(1.5+sin(u*5/3)/2)
z= sin(v)+2*cos(u*5/3)
umin= 0.0, umax= 20
vmin= -pi. vmax= pi
30Penne Rigate pastaSG Parplot Sample 030Frank Baumanncolor_modes 0-3
x= 0.1*cos(u)
y= -0.1*sin(u)
z= v+0.1*sin(u)
umin= 0.0, umax= 2 * pi
vmin= -0.5, vmax= 0.5
31Conchiglie RigateSG Parplot Sample 031Frank Baumannx= (u/(pi+pi))*(1.0-2.0*v*v)*cos(u)
y= (u/(pi+pi))*(1.0-2.0*v*v)*sin(u)
z= v
umin= 0.5235988, umax= 6.8067841
vmin= -0.5, vmax= 0.5
32Cavatappi (corkscrew)SG Parplot Sample 032Frank Baumannx= (3+2*cos(v))*cos(u)
y= (3+2*cos(v))*sin(u)
z= 1*u+2*sin(v)
umin= -12.5663706, umax= 2 * pi
vmin= 0.0, vmax= 2 * pi
33Farfalle(Bow-tie)SG Parplot Sample 033Frank Baumannx= u+(1/10)*sin(10*v)
y= ((2.0*v)/3.0)*(1.2-(1.0/(1.0+u*u)))
z= sin(pi*v)/(2*pi*v)
umin= -3, umax= 3
vmin= -pi, vmax= pi
34FusilliSG Parplot Sample 034Frank Baumanncolor_modes 1-3
x= (v/3)*cos(u-(2*1*pi)/3)
y= (v/3)*sin(u-(2*1*pi)/3)
z= u/10+(v^2)/2
umin= -2 * pi, umax= 2 * pi
vmin= 0.0, vmax= 0.5
35Under the seaSG Parplot Sample 035Don Towncolor_mode=2
x=u*cos(v)
y=u*sin(v)
z=exp(-u*u)*(sin(param_a*pi*(u))-u*cos(param_b*v))1
umin=0, umax=2
vmin=0,vmax=2 pi
1Set these values: param_a,param_b, to make changes
A, front and B, back: param_a=0 and param_b=0.
C: param_a=1 and param_b=1.
D: param_a=0 and param_b=1.
E: param_a=1 and param_b=0.
36ParallelogramSG Parplot Sample 036Don Townx=u*cos(v)
y=u*sin(v)
z=exp(-u*u)*(sin(param_a*pi*(u))-u*cos(param_b*v))
umin=0, umax=2
vmin=0,vmax=2 pi
A, B and D: param_a=2 and param_b=5.
C: param_a=-5 and param_b=5.
37Sine wave surfaceParplot Sample 037
38EllipticConeParplot Sample 038
39Ellipsoid (Change (0,0) to create ovoidParplot Sample 039
40Crossbar TwistParplot Sample 040
41Rippled RibbonParplot Sample 041
42Channel SurfaceParplot Sample 042
43Wavy surfaceParplot Sample 043
44Rippled surfaceParplot Sample 044
45Furled surfaceParplot Sample 045
46Accordian surfaceParplot Sample 046

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