# 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.

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 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
3torusAndreas 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
4helixAndreas 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 discAndreas 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 bottleAndreas 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 â€“ pi, umax = pi
vmin = 0.0 â€“ pi, vmax = 2.0 * pi
7Case 7Andreas 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 9Andreas Maschkex= = u*cos(v)
y = v*cos(u)
z = u*v*sin(u)*sin(v)
umin = 0.0 â€“ pi, umax = pi
vmin = 0.0 â€“ pi, vmax = pi
9Hershey KissAndreas 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 10Andreas 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 sphereAndreas 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
12ShellDimitri 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

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
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 spiralFrank 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 roseFrank 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 boxFrank 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 heartFrank 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 ShapeFrank 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 GumFrank 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 TorusFrank 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
22VaseFrank 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
23BreatherFrank 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)
24LissajousFrank 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 mushroomFrank 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 trefoilFrank 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#1Frank 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#2Frank 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 knotFrank 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 pastaFrank 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 RigateFrank 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
34FusilliFrank 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
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.
36ParallelogramDon 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