Definitions, derivations, notes, and long tables start folded.
The first eight are Splat Equation's own programs; the rest are small ideas to copy and
change. Each button opens the Splash with that program; then tap it to play t.
While the Splash is being tried out, it is on the shelf only when Splashery is opened with
?labs=1, but these links always open it.
A sphere from two angles, u around and v from pole to pole, spinning with u + t. Six stripes from floor(6u/(2pi)).
x = sin(v)cos(u + t)
y = cos(v)
z = sin(v)sin(u + t)
u = 0 .. 2pi
v = 0 .. pi
hue = floor(6u/(2pi))/6 + 0.04
size = 0.035
count = 7000
A tube around a ring. v + t rolls the tube around itself, so it turns inside out as you watch.
x = (2 + cos(v + t))cos(u)
y = sin(v + t)
z = (2 + cos(v + t))sin(u)
u = 0 .. 2pi
v = 0 .. 2pi
hue = v/(2pi)
size = 0.09
count = 6000
A band with a half twist: cos(u/2) turns the band over once as u goes around. The colors flow along it.
x = (1 + v cos((u + t)/2))cos(u + t)
y = v sin((u + t)/2)
z = (1 + v cos((u + t)/2))sin(u + t)
u = 0 .. 2pi
v = -0.4 .. 0.4
hue = u/(2pi)
size = 0.035
count = 4000
A tube that grows by exp(0.1u) as it winds three times around, turning with u + t. Its splats grow too.
x = exp(0.1u)cos(u + t)(1.2 + cos v)
y = exp(0.1u)(sin(v) - 2.4) + 3
z = exp(0.1u)sin(u + t)(1.2 + cos v)
u = 0 .. 6pi
v = 0 .. 2pi
hue = 0.02 + 0.1u/(6pi) + 0.03cos(4u)
size = 0.14exp(0.1u)
count = 10000
The simplest real knot, a curve in u alone, turned about the vertical by the rotation formulas in t.
x = (sin(u) + 2sin(2u))cos(t) - sin(3u)sin(t)
y = cos(u) - 2cos(2u)
z = -(sin(u) + 2sin(2u))sin(t) - sin(3u)cos(t)
u = 0 .. 2pi
v = 0 .. 1
hue = u/(2pi)
size = 0.16
count = 2500
A flat sheet in u and v with ripples running out from the middle: sin(distance − t).
x = u
y = 0.45sin(2sqrt(u^2 + v^2) - t)
z = v
u = -3 .. 3
v = -3 .. 3
hue = 0.58 - 0.07sin(2sqrt(u^2 + v^2) - t)
size = 0.07
count = 6000
Two arms from floor(v) (0 or 1, half a turn apart), scattered at random, turning once. Colors from r, g, and b.
x = u^1.5 cos(pi floor(v) + 5u + 1.2(v - floor(v)) - t)
y = 0.06(1 - u)sin(91v + 37u)
z = u^1.5 sin(pi floor(v) + 5u + 1.2(v - floor(v)) - t)
u = 0.02 .. 1
v = 0 .. 2
r = 0.55 + 0.45(1 - u)^2
g = 0.62 + 0.33(1 - u)^2
b = 1 - 0.45(1 - u)^3
size = 0.006 + 0.012(1 - u)^2
count = 10000
spread = random
The figure-eight Klein bottle: a figure-eight tube around a ring, with a half twist, so it has no inside or outside.
x = (2 + cos(u/2)sin(v + t) - sin(u/2)sin(2v + 2t))cos(u)
y = sin(u/2)sin(v + t) + cos(u/2)sin(2v + 2t)
z = (2 + cos(u/2)sin(v + t) - sin(u/2)sin(2v + 2t))sin(u)
u = 0 .. 2pi
v = 0 .. 2pi
hue = v/(2pi)
size = 0.13
count = 8000
The smallest program: one loop of u makes a ring of 200 splats. No v, no t.
x = cos(u)
y = sin(u)
z = 0
u = 0 .. 2pi
hue = u/(2pi)
size = 0.06
count = 200
Three turns of a helix whose height breathes with sin(t).
x = cos(u)
y = (0.09 + 0.035sin(t))u - 0.9
z = sin(u)
u = 0 .. 6pi
hue = 0.08 + u/(6pi)/3
size = 0.07
count = 1500
A famous heart curve, filled in by v from the middle out, beating twice per cycle.
x = v(1 + 0.08sin(2t))16sin(u)^3
y = v(1 + 0.08sin(2t))(13cos(u) - 5cos(2u) - 2cos(3u) - cos(4u))
z = 0
u = 0 .. 2pi
v = 0 .. 1
hue = 0.97 + 0.04v
size = 0.35
count = 4000
Color from r, g, and b: three cosines about a third of a turn apart make a rainbow along u.
x = u
y = 0.4sin(2u - t)
z = v
u = -3 .. 3
v = -0.4 .. 0.4
r = 0.5 + 0.5cos(u)
g = 0.5 + 0.5cos(u - 2)
b = 0.5 + 0.5cos(u + 2)
size = 0.05
count = 4000
Splats scattered at random over a sphere (v is the height, from −1 to 1) fly out, droop, and come back.
x = (0.2 + sin(t/2))sqrt(1 - v^2)cos(u)
y = (0.2 + sin(t/2))v - 0.35sin(t/2)^2
z = (0.2 + sin(t/2))sqrt(1 - v^2)sin(u)
u = 0 .. 2pi
v = -1 .. 1
hue = u/(2pi)
size = 0.018
count = 3000
spread = random
Five petals from cos(5u), and a cup that opens and closes with sin(t/2).
x = v(0.6 + 0.4cos(5u))cos(u)
y = (0.15 + 0.6sin(t/2))v^2
z = v(0.6 + 0.4cos(5u))sin(u)
u = 0 .. 2pi
v = 0 .. 1
hue = 0.92 - 0.12v
size = 0.035
count = 5000
A shape without t stands still, so a tap draws its splats again one by one, in the order they are made.
x = (0.5 + 0.2sin(3v))cos(u)
y = v
z = (0.5 + 0.2sin(3v))sin(u)
u = 0 .. 2pi
v = 0 .. 2.2
hue = 0.55 + 0.05sin(12u)
size = 0.045
count = 4000A second gallery, in six groups of ten. Each program reads, builds, and looks like its title. A few are honest look-alikes or samples of a named system, and say so; none is a full solution of the system it names. Each card has the picture, one line about the shape, the program (folded), and a Run it link that opens the Splat Equation Splash with that program, in a new tab. That Splash is a labs Splash: it is not on the ordinary shelf, but a direct link like these opens it even with labs off, and its sharper kernel setting needs labs turned on. Every program fits the Splash's own limits: 12 fields, 240 characters to an expression (each end of a range counts on its own; these programs are all under 120), and at most 10,000 points.
A sphere turns once around its vertical axis, and its hue runs around the axis (by longitude), so the colors turn with it.
x = sin(v)cos(u+t)
y = cos(v)
z = sin(v)sin(u+t)
u = 0 .. 2pi
v = 0 .. pi
hue = u/(2pi)
size = 0.04
count = 6000Run it (a labs Splash) About the shape
A round tube wraps around a ring as its colors follow the small circle.
x = (2+0.55cos(v))cos(u)
y = 0.55sin(v)
z = (2+0.55cos(v))sin(u)
u = 0 .. 2pi
v = 0 .. 2pi
hue = v/(2pi)
size = 0.05
count = 7000Run it (a labs Splash) About the shape
A narrow band turns through one half twist before its edges meet.
x = (1+vcos(u/2))cos(u)
y = vsin(u/2)
z = (1+vcos(u/2))sin(u)
u = 0 .. 2pi
v = -0.32 .. 0.32
hue = u/(2pi)
size = 0.035
count = 5000Run it (a labs Splash) About the shape
This immersed Klein bottle is a figure-eight tube that crosses itself along a ring.
x = (2+cos(u/2)sin(v)-sin(u/2)sin(2v))cos(u)
y = sin(u/2)sin(v)+cos(u/2)sin(2v)
z = (2+cos(u/2)sin(v)-sin(u/2)sin(2v))sin(u)
u = 0 .. 2pi
v = 0 .. 2pi
hue = v/(2pi)
size = 0.07
count = 10000Run it (a labs Splash) About the shape
Two tractrix horns meet at a sharp rim: a surface that curves the opposite way from a sphere.
x = cos(u)/cosh(v)
y = 1.2(v-tanh(v))
z = sin(u)/cosh(v)
u = 0 .. 2pi
v = -2.6 .. 2.6
hue = 0.55+0.2v/2.6
size = 0.05
count = 10000Run it (a labs Splash) About the shape
A simple polynomial surface curls into spreading lobes.
x = u-u^3/3+uv^2
y = v-v^3/3+vu^2
z = u^2-v^2
u = -1.6 .. 1.6
v = -1.6 .. 1.6
hue = 0.55+0.1sin(4u)
size = 0.07
count = 10000Run it (a labs Splash) About the shape
A catenoid pinches between two wide circular rims.
x = 0.45cosh(v)cos(u)
y = 0.45v
z = 0.45cosh(v)sin(u)
u = 0 .. 2pi
v = -1.6 .. 1.6
hue = 0.55+0.1v
size = 0.035
count = 7000Run it (a labs Splash) About the shape
A finite ruled helicoid patch winds like a ramp around the Z axis, with a helical edge on its outer rim.
x = vcos(u)
y = vsin(u)
z = 0.18u
u = -3pi .. 3pi
v = -1 .. 1
hue = 0.55+0.12sin(u)
size = 0.035
count = 7000Run it (a labs Splash) About the shape
Dini’s surface twists a trumpet shape into a tight spiral.
x = 0.65cos(u)sin(v)
y = 0.65sin(u)sin(v)
z = 0.65(cos(v)+log(tan(v/2)))+0.12u
u = 0 .. 4pi
v = 0.18 .. 2.95
hue = u/(4pi)
size = 0.03
count = 8000Run it (a labs Splash) About the shape
A logarithmic tube grows wider as it winds away from its narrow tip.
x = exp(0.12u)(1+0.35cos(v))cos(u)
y = exp(0.12u)(1+0.35cos(v))sin(u)
z = exp(0.12u)(0.35sin(v))
u = 0 .. 6pi
v = 0 .. 2pi
hue = u/(6pi)
size = 0.04+0.01u
count = 10000Run it (a labs Splash) About the shape
Four frequencies (2, 3, 4, and 7) trace a closed space curve that crosses itself, with a fine bead tube.
x = sin(3u+t)+0.16cos(7u)
y = 0.12cos(2u)
z = cos(4u+t)+0.16sin(7u)
u = 0 .. 2pi
v = 0 .. 1
hue = u/(2pi)
size = 0.045
count = 3200Run it (a labs Splash) About the shape
A tube follows the classic three-crossing trefoil knot and rotates in place.
x = (sin(u)+2sin(2u))cos(t)-sin(3u)sin(t)
y = cos(u)-2cos(2u)
z = -(sin(u)+2sin(2u))sin(t)-sin(3u)cos(t)
u = 0 .. 2pi
v = 0 .. 1
hue = u/(2pi)
size = 0.08
count = 3000Run it (a labs Splash) About the shape
Five over-and-under crossings wind around a torus in this thicker knot.
x = (2+0.35cos(5u))cos(2u+t)
y = 0.35sin(5u)
z = (2+0.35cos(5u))sin(2u+t)
u = 0 .. 2pi
v = 0 .. 1
hue = u/(2pi)
size = 0.055
count = 3500Run it (a labs Splash) About the shape
The curve cos(6u) traced in a plane makes a rose of 12 petals (an even multiple makes twice as many), and a gentle vertical wave lifts it into a dotted three-dimensional curve.
x = cos(6u)cos(u)
y = 0.15sin(3u)
z = cos(6u)sin(u)
u = 0 .. 2pi
v = 0 .. 1
hue = u/(2pi)
size = 0.04
count = 3000Run it (a labs Splash) About the shape
This closed string of beads traces a trefoil, the simplest knot (a torus knot that wraps three times one way and twice the other).
x = (2+cos(2u))cos(3u+t)
y = sin(2u)
z = (2+cos(2u))sin(3u+t)
u = 0 .. 2pi
v = 0 .. 1
hue = u/(2pi)
size = 0.05
count = 3500Run it (a labs Splash) About the shape
Two spiral strands wind together around a long axis.
x = 1.1cos(3u+pi floor(2v))
y = 1.4(u/pi-1)
z = 1.1sin(3u+pi floor(2v))
u = 0 .. 2pi
v = 0 .. 1
hue = 0.02+0.3floor(2v)+0.1u/(2pi)
size = 0.09
count = 10000
spread = randomRun it (a labs Splash) About the shape
A spring winds upward in eight turns as a narrow ribbon.
x = (1+0.08v)cos(u)
y = 0.1u+0.08vcos(u/8)
z = (1+0.08v)sin(u)
u = 0 .. 16pi
v = -1 .. 1
hue = u/(16pi)
size = 0.035
count = 5000Run it (a labs Splash) About the shape
This butterfly loop is a Lorenz-like look-alike, not a Lorenz-system solution.
x = 2.4sin(u)
y = 1.5sin(2u)+0.25sin(6u)
z = 1.1cos(u)+0.3cos(3u)
u = 0 .. 2pi
v = 0 .. 1
hue = u/(2pi)
size = 0.07
count = 4000Run it (a labs Splash)
A looping spiral suggests a Rössler attractor but is only a parametric look-alike.
x = cos(u)+0.35cos(7u)
y = sin(u)+0.35sin(7u)
z = 0.45sin(3u)
u = 0 .. 2pi
v = 0 .. 1
hue = u/(2pi)
size = 0.045
count = 3000Run it (a labs Splash)
Five broad petals rise from a shallow cup around a small center.
x = v(0.55+0.45cos(5u))cos(u)
y = 0.5v^2+0.1cos(5u)
z = v(0.55+0.45cos(5u))sin(u)
u = 0 .. 2pi
v = 0 .. 1
hue = 0.9-0.12v
size = 0.035
count = 6000Run it (a labs Splash) About the shape
A face-on disk shades from dark seeds to a golden rim, with Fibonacci-style spiral arms drawn in the color.
x = 1.8sqrt(u)cos(2pi v)
y = 1.8sqrt(u)sin(2pi v)
z = 0.25(1-u)
u = 0.002 .. 1
v = 0 .. 1
r = 0.3+0.7sqrt(u)(0.75+0.25sin(26pi v-24sqrt(u)))
g = 0.15+0.6sqrt(u)(0.75+0.25sin(26pi v-24sqrt(u)))
b = 0.02+0.1u
size = 0.04
count = 10000Run it (a labs Splash) About the shape
A widening spiral tube evokes a nautilus shell with a visible open center.
x = exp(0.13u)(1+0.3cos(v))cos(u)
y = 0.3exp(0.13u)sin(v)
z = exp(0.13u)(1+0.3cos(v))sin(u)
u = 0 .. 5pi
v = 0 .. 2pi
hue = 0.04+0.12u/(5pi)
size = 0.035+0.008u
count = 10000Run it (a labs Splash) About the shape
A dome-like bell pulses as its rim widens and narrows once each cycle.
x = (0.9+0.12sin(t))sin(v)(1+0.1cos(8u)sin(v)^6)cos(u)
y = 0.9cos(v)-0.2
z = (0.9+0.12sin(t))sin(v)(1+0.1cos(8u)sin(v)^6)sin(u)
u = 0 .. 2pi
v = 0 .. 0.6pi
hue = 0.82+0.05cos(8u)-0.1v
size = 0.05
count = 10000Run it (a labs Splash) About the shape
Branching sine ribs spread across a fan-shaped sheet.
x = vcos(u)
y = 0.16sin(9u+2v)
z = vsin(u)
u = -1.3 .. 1.3
v = 0 .. 1.8
hue = 0.03+0.08sin(9u+2v)
size = 0.025
count = 7000Run it (a labs Splash) About the shape
Scales follow a Fibonacci angle and taper toward the top of the cone.
x = (0.9-0.65v)(1+0.09sin(16pi u+25v)sin(26pi u-25v))cos(2pi u+2.4v)
y = 1.8v
z = (0.9-0.65v)(1+0.09sin(16pi u+25v)sin(26pi u-25v))sin(2pi u+2.4v)
u = 0 .. 1
v = 0 .. 1
hue = 0.07+0.05v+0.025sin(16pi u+25v)sin(26pi u-25v)
size = 0.045
count = 10000Run it (a labs Splash) About the shape
Curled arms rise from a low base like a ring of waving tentacles.
x = (0.25+0.55v)cos(u+0.3sin(3u))
y = v(1+0.18sin(5u))
z = (0.25+0.55v)sin(u+0.3sin(3u))
u = 0 .. 2pi
v = 0 .. 1
hue = 0.82+0.08sin(5u)
size = 0.03
count = 6000Run it (a labs Splash) About the shape
A central stem and repeated leaflets make a simple fern-like frond.
x = u
y = 0.08sin(7piu)
z = v(0.15+0.65abs(sin(7piu)))
u = -1 .. 1
v = 0 .. 1
hue = 0.28+0.12v
size = 0.025
count = 6500Run it (a labs Splash) About the shape
Layered radial petals alternate in height to form a dense dahlia-like flower.
x = v(0.4+0.6abs(cos(12u)))cos(u)
y = 0.25sin(12u)*v
z = v(0.4+0.6abs(cos(12u)))sin(u)
u = 0 .. 2pi
v = 0 .. 1
hue = 0.88+0.1cos(12u)
size = 0.025
count = 8000Run it (a labs Splash) About the shape
A flat branching fan uses nested waves to suggest coral growth.
x = vcos(u)
y = 0.12sin(11u)
z = vsin(u)
u = -1.5 .. 1.5
v = 0 .. 1.5
hue = 0.48+0.1sin(11u)
size = 0.028
count = 6500Run it (a labs Splash) About the shape
A scalloped circular leaf floats on a softly raised surface.
x = v(1+0.04cos(24u))cos(u)
y = 0.3v^3+0.12v
z = v(1+0.04cos(24u))sin(u)
u = 0.3 .. 2pi
v = 0 .. 1.2
hue = 0.3+0.04cos(14u)-0.05v
size = 0.06
count = 10000Run it (a labs Splash) About the shape
Concentric ripples travel across a square sheet without breaking at the cycle seam.
x = u
y = 0.38sin(2sqrt(u^2+v^2)-t)
z = v
u = -2.8 .. 2.8
v = -2.8 .. 2.8
hue = 0.58-0.08sin(2sqrt(u^2+v^2)-t)
size = 0.09
count = 10000Run it (a labs Splash) About the shape
The major and minor radii expand together and return once per cycle.
x = (1.7+0.45cos(v))(1+0.12sin(t))cos(u)
y = 0.45(1+0.12sin(t))sin(v)
z = (1.7+0.45cos(v))(1+0.12sin(t))sin(u)
u = 0 .. 2pi
v = 0 .. 2pi
hue = v/(2pi)
size = 0.045
count = 6500Run it (a labs Splash) About the shape
A saddle ripple rotates smoothly over a square patch.
x = u
y = 0.22(u^2-v^2)cos(t)+0.2uvsin(t)
z = v
u = -1.6 .. 1.6
v = -1.6 .. 1.6
hue = 0.6+1.2(0.22(u^2-v^2)cos(t)+0.2uvsin(t))
size = 0.06
count = 10000Run it (a labs Splash) About the shape
One loop circles the center while a smaller wave on it, with three times as many crests around the loop, turns the other way.
x = cos(u+t)+0.35cos(3u-t)
y = 0.35sin(3u-t)
z = sin(u+t)
u = 0 .. 2pi
v = 0 .. 1
hue = u/(2pi)
size = 0.045
count = 4500Run it (a labs Splash) About the shape
Petals lift and flatten in a smooth repeating bloom.
x = v(0.55+0.45cos(5u))cos(u)
y = (0.12+0.45(1+sin(t))/2)v^2
z = v(0.55+0.45cos(5u))sin(u)
u = 0 .. 2pi
v = 0 .. 1
hue = 0.9-0.1v
size = 0.03
count = 6000Run it (a labs Splash) About the shape
Four-fold bumps grow and shrink across a round surface as its color follows each bump.
x = sin(v)cos(u)(1+0.2cos(4u)cos(4v)sin(t+1.2))
y = cos(v)(1+0.2cos(4u)cos(4v)sin(t+1.2))
z = sin(v)sin(u)(1+0.2cos(4u)cos(4v)sin(t+1.2))
u = 0 .. 2pi
v = 0 .. pi
hue = 0.6+0.5cos(4u)cos(4v)sin(t+1.2)
size = 0.05
count = 10000Run it (a labs Splash) About the shape
A narrow ribbon rotates its cross-section through one full turn each cycle.
x = u
y = 1.1vcos(2u+t)
z = 1.1vsin(2u+t)
u = -2.4 .. 2.4
v = -1 .. 1
hue = 0.5+0.25v+0.1u
size = 0.06
count = 10000Run it (a labs Splash) About the shape
Five radial points breathe in and out with the beat of a sine wave.
x = 1.8v(0.65+0.16sin(t))(0.45+0.55(1-abs(sin(2.5u))))cos(u)
y = 1.8v(0.65+0.16sin(t))(0.45+0.55(1-abs(sin(2.5u))))sin(u)
z = 0.3(1-v)
u = 0 .. 2pi
v = 0 .. 1
hue = 0.1+0.08v+0.04sin(t)
size = 0.05
count = 10000Run it (a labs Splash) About the shape
A helix sways side to side and returns to its starting pose each cycle.
x = cos(u+t)
y = 0.12u
z = sin(u+t)+0.2sin(t)
u = 0 .. 8pi
v = 0 .. 1
hue = u/(8pi)
size = 0.04
count = 5000Run it (a labs Splash) About the shape
A rectangular sheet ripples in place with a standing two-axis wave.
x = u
y = 0.35sin(2u)sin(2v)cos(t)
z = v
u = -2 .. 2
v = -2 .. 2
hue = 0.62+0.12sin(2u)sin(2v)
size = 0.065
count = 10000Run it (a labs Splash) About the shape
A ridged surface assigns a full rainbow cycle to its height.
x = u
y = 0.3sin(4u+3v)
z = v
u = -2 .. 2
v = -2 .. 2
hue = (sin(4u+3v)+1)/2
size = 0.04
count = 6000Run it (a labs Splash) About the shape
Hue runs once around the large ring, so each slice across the tube has one color.
x = (1.5+0.4cos(v))cos(u)
y = 0.4sin(v)
z = (1.5+0.4cos(v))sin(u)
u = 0 .. 2pi
v = 0 .. 2pi
hue = u/(2pi)
size = 0.04
count = 6500Run it (a labs Splash) About the shape
Nested sine ridges color a saddle with a pattern that suggests changing curvature.
x = u
y = 0.15(u^2-v^2)
z = v
u = -2 .. 2
v = -2 .. 2
hue = 0.5+0.2sin(3u)cos(3v)
size = 0.035
count = 6500Run it (a labs Splash) About the shape
Red rises with height, green follows the horizontal angle, and blue fills the valleys.
x = cos(u)(1+0.2v)
y = v
z = sin(u)(1+0.2v)
u = 0 .. 2pi
v = -1 .. 1
r = 0.55+0.35v
g = 0.5+0.4sin(u)
b = 0.55-0.3v
size = 0.04
count = 6000Run it (a labs Splash) About the shape
A growing shell carries a rainbow gradient from its narrow tip to its wide lip.
x = exp(0.1u)cos(u)(1+0.25cos(v))
y = exp(0.1u)0.25sin(v)
z = exp(0.1u)sin(u)(1+0.25cos(v))
u = 0 .. 6pi
v = 0 .. 2pi
hue = u/(6pi)
size = 0.04+0.01u
count = 10000Run it (a labs Splash) About the shape
An RGB gradient moves from deep blue at the bottom to green at the top.
x = sin(v)cos(u)
y = cos(v)
z = sin(v)sin(u)
u = 0 .. 2pi
v = 0 .. pi
r = 0.05
g = 0.1+0.85(1+cos(v))/2
b = 0.15+0.8(1-cos(v))/2
size = 0.05
count = 10000Run it (a labs Splash) About the shape
Alternating bands run around the immersed bottle and make its crossing easy to see.
x = (2+cos(u/2)sin(v)-sin(u/2)sin(2v))cos(u)
y = sin(u/2)sin(v)+cos(u/2)sin(2v)
z = (2+cos(u/2)sin(v)-sin(u/2)sin(2v))sin(u)
u = 0 .. 2pi
v = 0 .. 2pi
hue = 0.5+0.25sin(4v)
size = 0.07
count = 10000Run it (a labs Splash) About the shape
Three offset waves make a smooth red, green, and blue color field.
x = u
y = 0.15sin(1.5u+1.5v)
z = v
u = -3 .. 3
v = -3 .. 3
r = 0.5+0.45sin(1.5u)
g = 0.5+0.45sin(1.5v+2)
b = 0.5+0.45sin(1.5u+1.5v+4)
size = 0.09
count = 10000Run it (a labs Splash) About the shape
A sphere is divided into twelve clean color wedges by its longitude.
x = sin(v)cos(u)
y = cos(v)
z = sin(v)sin(u)
u = 0 .. 2pi
v = 0 .. pi
hue = floor(12u/(2pi))/12
size = 0.035
count = 7000Run it (a labs Splash) About the shape
A moving ripple shifts both the sheet height and its rainbow colors.
x = u
y = 0.35sin(2u+v-t)
z = v
u = -3 .. 3
v = -3 .. 3
hue = 0.5+0.2sin(2u+v-t)
size = 0.04
count = 7000Run it (a labs Splash) About the shape
Warm colors gather near the core and cool colors trail along the spiral arms.
x = u cos(v+5u)
y = 0.12sin(13v+4u)
z = u sin(v+5u)
u = 0.02 .. 1
v = 0 .. 2
hue = 0.02+0.55u
size = 0.018
count = 9000
spread = randomRun it (a labs Splash) About the shape
Two circles pass through each other once, the simplest link, drawn as two dotted rings in different colors.
x = 1.6(1-floor(2v))cos(u)+floor(2v)(1.6cos(u)+1.6)-0.8
y = 1.6(1-floor(2v))sin(u)
z = 1.6floor(2v)sin(u)
u = 0 .. 2pi
v = 0 .. 1
hue = 0.02+0.55floor(2v)+0.1u/(2pi)
size = 0.14
count = 10000
spread = randomRun it (a labs Splash) About the shape
Three rotating harmonics add into one closed curve with a small bead radius.
x = cos(u)+0.45cos(3u)+0.2cos(5u)
y = 0.18sin(7u)
z = sin(u)+0.45sin(3u)+0.2sin(5u)
u = 0 .. 2pi
v = 0 .. 1
hue = u/(2pi)
size = 0.04
count = 3500Run it (a labs Splash) About the shape
Fourth-power rounding turns a sphere into a soft box with six flattened faces.
x = 1.6cos(u)cos(v)/((cos(u)^4+sin(u)^4)^0.25(cos(v)^4+sin(v)^4)^0.25)
y = 1.6sin(v)/(cos(v)^4+sin(v)^4)^0.25
z = 1.6sin(u)cos(v)/((cos(u)^4+sin(u)^4)^0.25(cos(v)^4+sin(v)^4)^0.25)
u = 0 .. 2pi
v = -pi/2 .. pi/2
hue = 0.5+0.3v/pi+0.1sin(u)
size = 0.06
count = 10000Run it (a labs Splash) About the shape
A square-root branch surface spirals through two sheets around its branch point.
x = sqrt(u)cos(v/2)
y = sqrt(u)sin(v/2)
z = 0.12v
u = 0.03 .. 1
v = 0 .. 4pi
hue = v/(4pi)
size = 0.03
count = 7000Run it (a labs Splash) About the shape
A cubic height field has three valleys meeting at one central saddle point.
x = u
y = 0.12(u^3-3uv^2)
z = v
u = -1.2 .. 1.2
v = -1.2 .. 1.2
hue = 0.55+0.1sin(3u)+0.2(u^3-3uv^2)
size = 0.05
count = 10000Run it (a labs Splash) About the shape
A spherical-harmonic-like radial formula gives the sphere four raised and lowered lobes.
x = (1+0.3sin(v)^2cos(4u))sin(v)cos(u)
y = (1+0.3sin(v)^2cos(4u))cos(v)
z = (1+0.3sin(v)^2cos(4u))sin(v)sin(u)
u = 0 .. 2pi
v = 0 .. pi
hue = 0.55+0.15cos(4u)
size = 0.035
count = 7000Run it (a labs Splash) About the shape
A tube wraps around a sideways figure eight with a subtle vertical wave.
x = cos(u)/(1+sin(u)^2)
y = 0.16sin(3u)
z = sin(u)cos(u)/(1+sin(u)^2)
u = 0 .. 2pi
v = 0 .. 1
hue = u/(2pi)
size = 0.05
count = 3000Run it (a labs Splash) About the shape
A height graph of one slice of the gyroid function rises and falls in a repeating pattern of hills and valleys.
x = u
y = 0.5(sin(u)cos(v)+0.36sin(v)+0.93cos(u))
z = v
u = -1.5pi .. 1.5pi
v = -1.5pi .. 1.5pi
hue = 0.55+0.3(sin(u)cos(v)+0.36sin(v)+0.93cos(u))
size = 0.11
count = 10000Run it (a labs Splash) About the shape
A (2,3) torus knot winds twice around the ring and three times around its tube.
x = (1+0.35cos(3u))cos(2u)
y = 0.35sin(3u)
z = (1+0.35cos(3u))sin(2u)
u = 0 .. 2pi
v = 0 .. 1
hue = u/(2pi)
size = 0.05
count = 3500Run it (a labs Splash) About the shape
Things to try. Change a number and see what moves. Swap cos and
sin. Put t somewhere new. Make count small and
size big to see the single splats. Try spread = random on a
surface. Give a sphere a hue of floor(8v/pi)/8.