# 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 lissajous Andreas 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
1cone Andreas 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)
24Lissajous 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
26Triangluoid 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 