Variation Types

Variation Types by Rick Sidwell

NameDimensionsNotesDC
apocarpet_js2D
arch2Dblur
asteria2D
atan2D
auger2D
barycentroid2D
bCollide2D
bent2D
bent22D
bi_linear2D
bipolar2D
blade2D
blade3D3D
blob2D
blob3D3Dsets z
blocky2D
blur2Dblur
blur_circle2Dblur
blur_linear2D
blur_pixelize2D
blur_zoom2D
blur3D3Dblur
bMod2D
boarders2D
boarders22D
brownian_js2D
bsplit2D
bSwirl2D
bTransform2D
bubble3Dsets z
bubble_wf3Dsets z
bubble23Dtransforms z
bubbleT3D3D
butterfly2D
butterfly_fay2D
butterfly3D3Dsets z
bwrands2D
bwraps72D
cannibiscurve_wf2Dblur
cardioid2D
cell2D
checkerboard_wf3DDC
checks2Dpasses z
chunk2D
circleblur2Dblur
circlecrop2Dpasses z
CircleLinear2D
CircleRand2Dblur
circlesplit2D
CircleTrans12D
circlize2D
circlize22D
circular2D
circular22D
circus2D
clifford_js2D
cloverleaf_wf2Dblur
collideoscope2D
colormap_wf3Dz onlyDC
colorscale_wf3Duses color
complex2D
conic2Dhalf blur
cos2D
cos2_bs2D
cosh2D
cosh2_bs2D
coshq3D
cosine2D
cosq3D
cot2D
cot2_bs2D
coth2D
coth2_bs2D
cothq3D
cotq3D
cpow2D
cpow22D
cpow32D
cpow3_wf2D
crackle2Dblur
crob2D
crop2Dpasses z
cross2D
crown_js3D
csc2D
csc2_bs2D
csch2D
csch2_bs2D
cschq3D
cscq3D
cubic3D3D
cubicLattice_3D3D
curl2D
curl_sp3D
curl3D3Dtransforms z
curve2D
custom_wf
custom_wf_full
cylinder2D
cylinder_apo3Dsets z
cylinder22D
d_spherical2D
dc_bubble3DDC
dc_carpet2DDC
dc_crackle_wf2DblurDC
dc_cracklep_wf2DblurDC
dc_cube3DblurDC
dc_cylinder3DDC
dc_cylinder23DDC
dc_hexes_wf2DDC
dc_linear2DDC
dc_perlin2DblurDC
dc_triangle2DDC
dc_triTile2Dblur
dc_ztransl3Duses color
deltaA2D
devil_warp2D
diamond2D
dinis_surface_wf3Dsets z
disc2D
disc22D
disc3D3Dtransforms z
displacemap_wf2DDC
dla_wf2Dblur
dla3D3DDC
dragon_js2Dblur
eclipse2D
eCollide2D
edisc2D
eJulia2D
elliptic2D
eMod2D
eMotion2D
ennepers2D
ennepers23D
Epispiral2Dhalf blur
epispiral_wf2D
ePush2D
erf2D
erf3D3D
eRotate2D
eScale2D
escher2D
estiq3D
eSwirl2D
ex2D
exblur3D
exp2D
exp2_bs2D
exponential2D
extrude3Dz only - sets Z
eyefish2D
falloff23Dtransforms z
falloff33D
fan2D
fan22D
farblur3D
fdisc2D
fibonacci22D
fisheye2D
flatten3Dz only - sets Z
flipcircle2D
flipy2D
flower2Dhalf blur
flower_db3D
flux2D
foci2D
foci_3D3D
fourth2D
fract_dragon_wf3DblurDC
fract_formula_julia_wf3DblurDC
fract_formula_mand_wf3DblurDC
fract_julia_wf3DblurDC
fract_mandelbrot_wf3DblurDC
fract_meteors_wf3DblurDC
fract_pearls_wf3DblurDC
fract_salamander_wf3DblurDC
funnel2D
gamma2D
gaussian_blur2Dblur
gdoffs2Dpasses z
glynnia2D
glynnia32D
GlynnSim12D
GlynnSim22D
GlynnSim32D
gosperisland_js2Dblur
grid3D3D
gridout2D
gridout22D
hadamard_js2Dblur
hamid_js2Dblur
handkerchief2D
harmonograph_js2Dblur
heart2D
heart_wf2D
helicoid3D
helix3D
hemisphere3Dsets z
hexaplay3D3D
hexes2D
hexnix3D3D
hilbert_js2Dblur
ho3D
hole22D
horseshoe2D
htree_js2Dblur
hyperbolic2D
hypershift2D
hypertile2D
hypertile12D
hypertile22D
hypertile3D3D
hypertile3D3D
hypertile3D3D
idisc2D
iflames_wf3DblurDC
inflateZ_13Dtransforms z only
inflateZ_23Dtransforms z only
inflateZ_33Dtransforms z only
inflateZ_43Dtransforms z only
inflateZ_53Dtransforms z only
inflateZ_63Dtransforms z only
inversion2D
invtree_js2D
isosfplot3D3DDC
jac_cn2D
jac_dn2D
jac_sn2D
jubiQ3D
julia2D
julia3D3Dtransforms z
julia3D3Dtransforms z
julia3D3Dtransforms z
Juliac2D
julian2D
julian22D
julian3D3D
juliaq2D
juliascope2D
Kaleidoscope2D
klein_group2D
koch_js2Dblur
lace_js2D
layered_spiral2D
lazyjess2D
lazysusan2D
lazyTravis2D
line3D
linear2D
linear3D3D
linearT2D
linearT3D3D
Lissajous2Dblur
log2D
log_apo2D
log_db2D
log_tile23D
loonie2D
loonie_3D3D
loonie22D
loonie32D
loq3D
lorenz_js3D
lsystem_js2Dblur
lsystem3D3Dblur
mandelbrot3Dblur
mask2D
maurer_lines3DDC
maurer_rose3DDC
mcarpet2D
minkowscope2D
minkQM2D
mobiq3D
mobius2D
mobius_strip3D
MobiusN2D
modulus2D
murl2D
murl22D
nBlur2Dblur
ngon2D
noise2Dhalf blur
npolar2D
obj_mesh_primitive_wf3Dmesh
obj_mesh_wf3Dmesh
octagon3D
onion3D
onion23D
ortho2D
oscilloscope2D
oscilloscope22D
ovoid3D3Dtransforms z
panorama12D
panorama22D
parabola2Dhalf blur
parplot2D3Dblur
pdj2D
perspective2D
petal2D
phoenix_julia2D
pie2Dblur
pie3D3Dblur
plane_wf3DDC
poincare3D3D
polar2D
polar22D
polylogarithm2D
popcorn2D
popcorn22D
popcorn2_3D3D
post_axis_symmetry_wf3D
post_bumpmap_wf3Dz only
post_bwraps22D
post_circlecrop2Dpasses z
post_colormap_wf3Dz onlyDC
post_colorscale_wf3Duses color
post_crop2Dpasses z
post_curl2D
post_curl3D3Dtransforms z
post_custom_wf
post_dcztransl3Duses color
post_depth3D
post_displacemap_wf2DDC
post_falloff23Dtransforms z
post_falloff33D
post_heat3Dtransforms z
post_julia3D3Dtransforms z
post_juliaq2D
post_mirror_wf3D
post_point_symmetry_wf2D
post_rblur2D
post_rotate_x3D
post_rotate_y3D
post_smartcrop3DDC
post_spherical2D
post_spin_z2D
post_zscale_wf3Dz only
post_ztranslate_wf3Dz only
pow_block2D
power2D
pre_blur2Dblur
pre_blur3D3Dblur
pre_boarders22D
pre_bwraps22D
pre_circlecrop2Dpasses z
pre_crop2Dpasses z
pre_curl2D
pre_custom_wf
pre_dcztransl3Duses color
pre_disc3D3Dtransforms z
pre_falloff33D
pre_rect_wf2Dblur
pre_rotate_x3D
pre_rotate_y3D
pre_sinusoidal3D3Dtransforms z
pre_spherical2D
pre_spin_z2D
pre_stabilize2D
pre_subflame_wf3DDC
pre_wave3D3D
pre_zscale3Dz only
pre_ztranslate3Dz only
pressure_wave2D
primitives_wf2D/3Dblur
pRose3D3Dhalf blur
quaternion3D
r_circleblur2D
radial_blur2Dhalf blur
rational32D
rays2D
rays12D
rays22D
rays32D
rectangles2D
rhodonea2D
rings2D
rings22D
ripple2D
rippled2D
rose_wf2D
rosoni2D
roundspher2D
roundspher3D3Dtransforms z
rsquares_js2Dblur
sattractor_js2D
scrambly2D
scry2D
scry_3D3Dtransforms z
scry22D
sec2D
sec2_bs2D
secant22D
sech2D
sech2_bs2D
sechq3D
secq3D
separation2D
shift2D
shredlin2D
shredrad2D
siercarpet_js2D
sigmoid2D
sin2D
sin2_bs2D
sineblur2Dblur
sinh2D
sinh2_bs2D
sinhq3D
sinq3D
sintrange2D
sinusoidal2D
sinusoidal3D3Dtransforms z
sph3D3D
sphere_nja3D
spherecrop3D
spherical2D
Spherical3D3Dtransforms z
spherical3D_wf3D
sphericalN2D
sphtiling3v22DDC
spiral2D
spiralwing2D
Spirograph2Dblur
spirograph3D3Dblur
spliptic_bs2D
split2D
SplitBrdr2D
splits2D
splits3D3D
square2Dblur
square3D3Dblur
squarize2D
squirrel2D
squish2D
starblur2Dblur
stripes2D
stwin2D
subflame_wf3DDC
super_shape2D
SuperShape3D3Dblur
svensson_js2D
svf3Dsets z
svg_wf2DDC
swirl2D
swirl32D
synth2D
tan2D
tan2_bs2D
tancos2D
tangent2D
tangent3D3Dsets z
tanh2D
tanh2_bs2D
tanhq3D
tanq3D
target2D
target_sp2D
taurus3D
text_wf2DblurDC
tile_hlp2D
tile_log2D
trade2D
tree_js2Dblur
Truchet2D
truchet_ae2DDC
Truchet_fill2D
twintrian2D
twoface2D
unpolar2D
vogel2D
voron2D
w2D
waffle2Dblur
wallpaper_js2D
waveblur_wf3DblurDC
waves2D
waves22D
waves2_3D3D
waves2_radial2D
waves2_wf2D
waves2b2D
waves3_wf2D
waves4_wf2D
wdisc2D
wedge2D
wedge_julia2D
wedge_sph2D
whitney_umbrella3D
whorl2D
woggle_js2D
x2D
xerf3D
xheart2D
xheart_blur_wf2Dblur
xtrb2D
y2D
yin_yang2D
yplot2D3DblurDC
yplot3D3DblurDC
z2D
zblur3DBlur - z only
zcone3Dz only
zscale3Dz only
ztranslate3Dz only
ztwister2Duses z
3D Variation list generously compiled by Rick Sidwell.

"There's a bit more than just 2D or 3D; "blur" means it ignores its inputs, DC is direct color. But they should all have 2D or 3D, based on whether or not the variation code assigns to z."

Notes:
Griffin Sarah
My particular rule of thumb has to do with what happens with pitch. If the transform flattens to a line at 90° it's 2D. and someone mentioned that even some 3D, like Bubbles don't behave well in 3D rendering or as variation 2 with other 3D labeled variations. otoh, many 2D variations look very interesting with extrude or curl nearby. I'm sorry, I've not had the time to make a systematic study.

Rick Sidwell
Bubble is really a 2D to 3D variation. It basically flattens the flame then maps the result to a sphere.

Crackle Presets

Crackle Preset Styles

#PresetName
0Default
1Blob
2Net
3Paving
4Texture
5Grid
6Mosaic
7Boxes
8Nebula
9Molecular
10Tiny Bubbles
11Med. Filled Boxes
12Big Boxes
13Very Big Boxes
14Shibori
15Scotch Mist
16Squared Grid
17Blocky
18Cubish
19Wired
20Mechano
A list of the Crackle Presets by Don Town

Isoplot 3D Presets

Isoplot 3D Presets

Preset IDName
0Default
1Blob
2Net
3Paving
4Texture
5Grid
6Mosaic
7Boxes
8Nebula
9Molecular
10Tiny Bubbles
11Med. Filled Boxes
12Big Boxes
13Very Big Boxes
14Shibori
15Scotch Mist
16Squared Grid
17Blocky
18Cubish
19Wired
20Mechano
A list of 3D Isoplot Formulae Presets by Don Town

Good As Second Variations

Good As Second Variations List

VariationGood?Info
archYes
asteriaYes
augerYes
barycentroidYes
bCollideYes
bentYes
bent2Yes
bi_linearYes
bipolarYes
bladeYes
blade3DYes
blobYes
blob3DYes
blockyYes
blur
blur_circle
blur_pixelize
blur_zoom
blur3D
bModYes
boardersYes
boarders2Yes
bsplitYes
bSwirlYes
bTransformYes
bubbleYes+ Regular
bubble_wfYes+ Regular
bubble2Yes
bubbleT3DYes
butterflyYes
butterfly_fay
butterfly3DYes
bwrandsYes
bwraps7Yes
cannabiscurve_wf
cellYes
checksYes
circleblur
circlecropYes
circlelinearYes
circlerand
circletrans1Yes
circlizeYes
circlize2Yes
circusYes
cloverleaf_wfYes
collidiscopeYes
colormap_wfYes
colorscale_wfYes
conic
cosYes
coshYes
cosineYes
cotYes
cothYes
cpowYes
cpow3Yes
crackle
cropYes
crossYes
cscYes
cschYes
cubic3DYesAdd extrude
cubicLattice_3DYesAdd extrude
curlYes
curl_spYes
curl3DYes
curveYes
custom_wf
cylinderYes
cylinder_apoYes
dc_bubbleYes
dc_carpet
dc_crackle_wf
dc_cube
dc_hexes_wfYes
dc_linearYes
dc_perlin
dc_triangleYes+ Regular
dc_ztranslYes
deltaAYes
devil_warpYes
diamondYes
dinis_surface_wfYes
discYes
disc2Yes
disc3DYes
displacemap_wfYes
dla_wf(diffusion-ltd aggregation)
eclipseYes
ecollideYes
ediscYes+ Regular
ejuliaYes+ Regular
ellipticYes
eModYes
eMotionYes
ennepersYes
ennepers2Yes+Regular
epispiralYes
epispiral_wfYes
epitrochoid
ePushYes
eRotateYes
eScaleYes
escher=drosteYes
eSwirlYes
exYes
exblur
expYes
exponentialYes
extrudeYes+Regular
eyefishYes
falloff2Yes
falloff3Yes
fanYes
fan2Yes
farblur
fdiscYes
fibonacci2
fisheyeYes
flattenYes+Regular
flipcircleYes
flipyYes
flower
flower_dbYes
fluxYes
fociYes
foci3DYes
fourthYes
fract_dragon_wf
fract_formula_julia_wf
fract_formula_mand_wf
fract_julia_wf
fract_mandelbrot_wf
fract_meteors_wf
fract_pearls_wf
fract_salemander_wf
funnelYesEffect=0
gaussian_blur
gdoffsYes
glynniaYes
glynnia3Yes
glynnSim1Yes
glynnSim2Yes
glynnSim3
grid3D_wfYes
handkerchiefYes
heartYes
heart_wfYes
hemisphereYes+Regular
hexaplay3DYes+Regular
hexesYes
hexnix3dYes
ho (hyperbolic octahedra)Yes
horseshoeYes
hyperbolicYes
hypertileYes
hypertile1Yes
hypertile2Yes
hypertile3DYes
hypertile3D1Yes
hypertile3D2Yes
hypotrochoid
idiscYes
inflateZ_1Yes+Regular
inflateZ_2Yes+Regular
inflateZ_3Yes+Regular
inflateZ_4Yes+Regular
inflateZ_5Yes+Regular
inflateZ_6Yes+Regular
jac_cnYes
jac_dnYes
jac_snYes
juliaYes
julia3dYes
julia3dzYes
juliacYes
julianYes
julian2Yes
julian3DxYes
juliaqYes
juliaq3DqYes
juliascopeYes
kaleidoscopeYes
layered_spiralYes
lazyjessYes
lazysusanYes
lazyTravisYes
lineYes
linearYes
linear3DYes
linearTYes
linearT3DYes
lissajousYes
logYes
log_apoYes
log_dbYes
loonieYes
loonie_3DYes
loonie2Yes
loonie3Yes
mandelbrot
maskYes
Maurer_Lines
Maurer_Rose
mcarpetYes
mobiusYes
mobius_stripYes
modulusYes
murlYes
murl2Yes
nBlur
ngonYes
noise
npolarYes
obj_mesh_primitivesYes
obj_mesh_wfYes
octagonYes
onionYes
onion2Yes
orthoYes
oscilloscopeYes
oscilloscope2Yes
ovoid3dYes
parabolaYes
pdjYes
perspectiveYes
petalYes
phoenix_juliaYes
pie
pie3d
poincare3DYes
polarYes
polar2Yes
polylogarithmYes
popcornYes
popcorn2Yes
popcorn2_3DYes
post_axis_symmetry_wfYes
post_bumpmap_wfYes
post_bwraps2Yes
post_circlecropYes
post_colormap_wfYes
post_colorscale_wfYes
post_cropYes
post_curlYes
post_curl3DYes
post_custom_wf
post_dcztranslYes
post_depth
post_displacemap_wfYes
post_falloff2Yes
post_falloff3Yes
post_heatYes
post_julia3DqYes
post_juliaqYes
post_mirror_wfYes
post_point_symmetry_wfYes
post_rblurYes
post_rotate_xYes
post_rotate_yYes
post_smartcropYes
post_spin_zYes
post_zscale_wfYes
post_ztranslateYes
pow_blockYes
powerYes
pre_blurYesAs Pre not post
pre_boarder2YesAs Pre not post
pre_bwraps2YesAs Pre not post
pre_circlecropYesAs Pre not post
pre_cropYesAs Pre not post
pre_curlYesAs Pre not post
pre_custom_wf
pre_dcztranslYesAs Pre not post
pre_disc3DYesAs Pre not post
pre_falloff3YesAs Pre not post
pre_rect_wfYesAs Pre not post
pre_rotate_xYesAs Pre not post
pre_rotate_yYesAs Pre not post
pre_sinusoidal3DYesAs Pre not post
pre_spin_zYesAs Pre not post
pre_subflame_wf
pre_waves3D_wfYesAs Pre not post
pre_zscaleYesAs Pre not post
pre_ztranslateYesAs Pre not post
primatives_wf
pRose3DYes
radial_blur
rational3Yes
rays
rays1Yes+Regular
rays2
rays3
rectanglesYes
rhodoneaYes
rings
rings2Yes
rippleYes
rippledYes
rose_wfYes
rosoniYes
roundspherYes
roundspher3DYes
scramblyYes
scryYes
scry_3DYes
scry2Yes
secYes
secant2Yes
sechYes
separationYes
shredlinYes
sinYes
sineblur
sinhYes
sintrangeYes
sinusoidalYes
sinusoidal3DYes
sph3DYes
sphere_njaYes
sphericalYes
spherical3DYes
spherical3D_wfYes
sphericalNYes
spiralYes
spiralwingYes
spirograph
splitYes
splitbrdrYes
splitsYes
splits3DYes
squareYes
square3DYes
squarizeYes
squirrelYes
squishYes
starblur
stripesYes
stwinYes
subflame_wf
super_shapeYes
superShape3DYes
svf (single value func.)Yes
svg_wf
swirlYes
synthYesNon-blur modes
synth2
tanYes
tancosYes
tangentYes
tangent3DYes
tanhYes
targetYes
target_spYes
taurusYes
text_wf
tradeYes
truchetYes
twintrianYes
twofaceYes
unpolarYes
vogelYes
voronYes
wYes
waffle
waveblur_wf
wavesYes
waves2Yes
waves2_3DYes
waves2_wfYes
waves2bYes
waves3_wfYes
waves4_wfYes
wdiscYes
wedgeYes
wedge_juliaYes
wedge_sphYes
whitney_umbrelaYes
whorlYes
xYes
xheartYes
xheart_blur_wf
xtrb=triboarder2Yes
yYes
yin_yangYes
zYes
zblur
zconeYes+Regular
zscaleYes+Regular
ztranslateYes+Regular
A quick list compiled by Don Town of variations that work well as second variations.

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 lissajous3D 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
1coneConeAndreas 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
2shellShell
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
3torusTorus
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
4helixHelix
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 discWavy 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 bottleKlein 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 7Parplot Presets SG Parplot Sample 07 150x150
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 9Parplot Presets SG Parplot Sample 08 150x150

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 KissHershey 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 10Parplot Presets SG Parplot Sample 010 150x150
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 sphereVarigated 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
12ShellShell
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
13SlinkySlinky
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 slinkyReal 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 spiralSpherical 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 roseSpherical 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 boxFolded 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 heartWavy 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 ShapeNameless #1
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 GumBubble 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 TorusTwisted 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
22VaseVase
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
23BreatherBreather
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 mushroomDouble 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 trefoilTrianguloid 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#1Shell #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#2Shell #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 knotTrefoil 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 pastaPenne 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 RigateConchiglie Pasta
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)Cavatappi
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)Farfalle
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
34FusilliFusilli
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 seaUnder 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.
36ParallelogramParallelogram
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 surfaceSine Wave Surface
38EllipticConeElliptic Cone
39Ellipsoid (Change (0,0) to create ovoidEllipsoid
40Crossbar TwistCrossbar Twist
41Rippled RibbonRippled Ribbon
42Channel SurfaceChannel Surface
43Wavy surfaceWavy Surface
44Rippled surfaceRippled Surface
45Furled surfaceFurled Surface
46Accordian surfaceAccordion Surface

LSystem 3D Presets

Lsystem 3D Presets

Preset NumberPreset Name
1Hilbert
2Paper tape
3Polyhedron
4Axis
5Spiral
6Sierpinski
7Shell
8Colors
9Hexahedron
10Octahedron
11Fern
12Horn
13Passie
14Leaves
15Menger Cube
16Spiral 1
17Boat
18Spiral plant
19Becker plant
20Cello
21Spider
A list of Lsystem 3D presets by Don Town.

LSystem Presets

Lsystem Presets

Preset#Shape Name
1Hilbert
2Koch
3KochIsland
4KochSnowflake
5Peano
6Sierpinski Carpet
7Sierpinski Triangle
8Alfonseca
9ADH155 (Anthony Hammer)
10Crystal
11Cross SC
12Fass1
13Hex-7-b
14Board
15Sphinx
16Pythagorean Tree
17Seaweed06
18Seaweed08
19Seaweed05
20Sapin3
21Root
22Plant08
23PlantsbyRoad
24Plant02b
25Leaves
A list of Lsystem presets compliled by Don Town.