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 ID | Preset | Example Image | Creator | Notes |
|---|---|---|---|---|
| 0 | 3D lissajous |  | Andreas Maschke | x=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 |
| 1 | cone |  | Andreas Maschke | color_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 |
| 2 | shell |  | Andreas Maschke | color_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 |
| 3 | torus |  | Andreas Maschke | xformula = 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 |
| 4 | helix |  | Andreas Maschke | color_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 |
| 5 | wavy disc |  | Andreas Maschke | x = 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 |
| 6 | klein bottle |  | Andreas Maschke | x = 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 |
| 7 | Case 7 |  | Andreas Maschke | x = 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 |
| 8 | Case 9 |  | Andreas Maschke | x= = 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 |
| 9 | Hershey Kiss |  | Andreas Maschke | x = 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 |
| 10 | Case 10 |  | Andreas Maschke | x`= 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 |
| 11 | Varigated sphere |  | Andreas Maschke | solid 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 |
| 12 | Shell |  | Dimitri Augusto Rocha | https://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 |
| 13 | Slinky |  | Don Town | http://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 |
| 14 | Real slinky |  | Frank Baumann | x=(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 |
| 15 | Spherical spiral |  | Frank Baumann | x= 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 |
| 16 | Spherical rose |  | Frank Baumann | xformula= (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 |
| 17 | Folded box |  | Frank Baumann | Preset_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 |
| 18 | Wavy heart |  | Frank Baumann | x= (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. |
| 19 | Interesting Shape |  | Frank Baumann | color_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 |
| 20 | Bubble Gum |  | Frank Baumann | xformula= 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 |
| 21 | Twisted Torus |  | Frank Baumann | xformula= (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 |
| 22 | Vase |  | Frank Baumann | xformula= 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 |
| 23 | Breather |  | Frank Baumann | color_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) |
| 24 | Lissajous |  | Frank Baumann | x= 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). |
| 25 | Double 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 |
| 26 | Trangluoid trefoil |  | Frank Baumann | color_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 |
| 27 | Shell#1 |  | Frank Baumann | color_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 |
| 28 | Shell#2 |  | Frank Baumann | color_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 |
| 29 | Trefoil knot |  | Frank Baumann | x= 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 |
| 30 | Penne Rigate pasta |  | Frank Baumann | color_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 |
| 31 | Conchiglie Rigate |  | Frank Baumann | x= (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 |
| 32 | Cavatappi (corkscrew) |  | Frank Baumann | x= (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 |
| 33 | Farfalle(Bow-tie) |  | Frank Baumann | x= 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 |
| 34 | Fusilli |  | Frank Baumann | color_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 |
| 35 | Under the sea |  | Don Town | color_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. |
| 36 | Parallelogram |  | Don Town | x=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. |
| 37 | Sine wave surface |  | ||
| 38 | EllipticCone |  | ||
| 39 | Ellipsoid (Change (0,0) to create ovoid |  | ||
| 40 | Crossbar Twist |  | ||
| 41 | Rippled Ribbon |  | ||
| 42 | Channel Surface |  | ||
| 43 | Wavy surface |  | ||
| 44 | Rippled surface |  | ||
| 45 | Furled surface |  | ||
| 46 | Accordian surface |  |
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