Parplot Presets

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.
~ed. slg
Preset IDPresetExample ImageCreatorNotes
03D lissajousAndreas 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
1coneAndreas 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
2shell
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
3torus
Andreas 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
4helix
Andreas 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 disc
Andreas 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 bottle
Andreas 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 7
Andreas 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 9

Andreas 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 Kiss
Andreas 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 10
Andreas 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 sphere
Andreas 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
12Shell
Dimitri 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
13Slinky
Don 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 slinky
Frank 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 spiral
Frank 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 rose
Frank 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 box
Frank 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 heart
Frank 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 Shape
Frank 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 Gum
Frank 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 Torus
Frank 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
22Vase
Frank 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
23Breather
Frank 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)
24LissajousLissajous
Frank 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 mushroom
Frank 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
26Trangluoid trefoil
Frank 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#1
Frank 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#2
Frank 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 knot
Frank 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 pasta
Frank 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 Rigate
Frank 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)
Frank 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)
Frank 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
34Fusilli
Frank 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 sea
Don 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.
36Parallelogram
Don 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 surface
38EllipticCone
39Ellipsoid (Change (0,0) to create ovoid
40Crossbar Twist
41Rippled Ribbon
42Channel Surface
43Wavy surface
44Rippled surface
45Furled surface
46Accordian surface

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