Try Lissajous 3D. You can play these animations as your screen saver, make more patterns of your own - and explore the patterns in 3D.

3d brushwork flower
a graceful dance
abstract art swirls
African shawl
airy bowl
almost symmetric basketwork
almost symmetry
alpine flower
angular
angular tri sprio
at ease
Autumnal colour leaf swoop
beach balls
Beguiled
Bessel Sailing Ship
Bessel swirl
bewildering spirals
bivalve
bivalve randomised
blobby
blotch
blue basketwork wheel
blue basketwork wheel with distortion
blue tinted quartz
breathing space
brown and blue flower shape
cave crystal
Chocolate box ribbon
circle dance crystals
circling pipes
circular wavform
colour harmony
Colour Ripples
colour warp
colourful
colourful pewter seven arm starfish
colourful spirograph
colourful whirlygig
concertina flower
consultation
convolutions
copper green
copper straw basket
copper whirlygig
coronet
crazy caterpillar
crazy hat
crazy machine
crazy star cogs
crescents
crinkle wheels
crinkly gold star
criss cross flower
crystal shards
curlicues
curved helix
dance of primary colours
dancing gold loop
day full of promise
Deep sea darting fish
desert rose crystal
diaphanous
diaton loops
dont know
double cup fungi
double flower bowl
doughnut
drifting spirograph
drifting spirograph three fold symmetry
Drifting wizard s star
driftwood tangle
early spring emerald flower
eccentric diamonds
eight
eight petal geometric flower
eludes capture
endlessly unravelling
escalate
evolving spirals
exotic blossom
Expressionist artefact
eye of the storm
fascination
fiery copper wheel
filligree copper
fine gauze
firework
flight
flip flop
flower effect
fluid motion
fluting
foggy archways
foggy ripply filligree copper
foggy ripply ripples
four pointed star wheels spiro
four wheel crinkly spirograph
frame
frog spawn
From a forgotten realm
garland
gausy flower
gentle cool spirograph
Gentle curves
gentle morph
geometric colourful flower
geometric pattern bowl
geometric pattern bowl-was
geometric spirograph efect
geometric spirograph transforming
glass jewel
glowing
glowing2
gold braided bowl
gold cascade
gold circlets
gold double double spiral
gold four petal flower
gold pearl twisted tube at sunset
gold tangle
gold whirlygig
golden spring
grass green symmetrical knot
gravitational encounter with spirograph
green bracelet
Hazy sea creature
heart throb
hug
hyper basket weave
hyper basket weave opalescent
hyper-snooker
icing
Iguana
Indian Red
intersections
inverse seventh power rule
Inverted spirograph
jade star
jellyfish
knobbly forest roots
knotty tangle
lantern glass
late autumn ruby flower
late autumn ruby flower2
layered mauve ribbon
Lazy Day
light show
Lilo
Lissajous spheres
lively red flower
log jam
magic flames
magic ribbon
magnetised golden spiral
magnetised Lissajous
magnetised Lissajous as dipole
magnetised rainbow spiral
marine gold
marooned
marshmallows
matted roots
maverick
meadow song
midnight rainbow concertina
midnight rose spirograph
midnight rose spirograph2
misty petals
misty petals2
misty pink
misty rose brightness and saturation ripples
morphing cd
morphing star
mountain vista
net
night pearls
nine petal star
nine point snowflake
obisidian gold cymbals
obisidian gold cymbals2
opalescent flower
orange rose
orchid
orchid petals
organised chaos
pale blue whirlygig
paper trail
Parrot colours
party hat
party streamer
passing by
pastel effect transparency
patchwork
patchwork cylinder
patchwork sculpture
pearl flower fretwork at sunset
pearl necklace at dawn
penta twist
perturbed
phoenix
pink rose
playful orange gold loop
playful origami
pointy pink star
pointy pink star2
Polished gold rope
pop art
pot-pourri
prickly green cactus
puzzly topology
quaternion morph
radius and width ripples
rainbow dancer
rainbow frame
rainbow ripples
rainbow rope game
rainbow tinted gold spirograph
red gold folded carpet
rhombi
ribbed gold ribbon
ringlets
ripples of light
ripply ribbon
robotoid
Roilling
rolly polly wheel
rose hued
rose hued 2
rosette
rosy drifting wheel spiro
rosy drifting wheel spiro2
rosy quartz
rosy spider
rosy swirl
ruby and gold broad ribbon
ruby emerald
ruby emerald star
ruby whale
scrap heap
sea flourish
sea urchin
seashore surprise
seven point snowflake
seventeen point snowflake
shape with magnet
shape with planet
shape with planet 1
shawl
shield shaped mauve spirograph
shocking pink strata
Simple 3D lissajous
Simple 3D lissajous inverted in sphere
six fold gold spiral
six fold gold spiral shield
six point drifting snowflake
six point drifting snowflake 2
sky dragon
sky hook
skyscraper
slythy toves
snowdrop
space creature
space flower
spiky
spiky flower
spin
spiral rays
spiral wheel
spirally gold white
spirally rainbow ribbon
spiro petals
spiro petals2
spiro spring
spiro twist
spirograph drifting rose
spirograph inverted
spirograph inverted2
splash
Spring copper beeches
spring shadows
square wheels spiro2
square wheels spirograph
square wheels spirograph inverted in sphere
squarish waves effect
stair rods
star
star ballet
star coaster
star hexagon creatures
star pipes
star polygon cross section
star skater
stepped ribbon of light
streaky ribbons
stretch
stripy
sunset tinted gold
super complex crinkly spirograph
swirily colours
test new random spiro
three wheel spirograph
tinged pearl necklace at dawn
tinged ruby basketwork spirograph
tinted bronze drifting spirograph
tinted bronze drifting spirograph2
tinted gold 3D spirograph in thunderstorm
tipsy poly
toroidal spiral
Trajectory
transforming pink twisty spiro sky diver
transforming water wheel
transforming water wheel with randomised drifts
translucent blue flower
translucent red and yellow rope
translucent ruby and gold beads
transparency hue saturation and brightmess ripples
transparent morphing cd
transparent red gold
transparent star
trefoil
Triangle pattern spirograph
triplet
tropical colours
turquoise star
Twisted brass
twisted star polygon visitors
twisty spiro circlet
twisty spirograph
twisty trefoil spirograph
two fold symmetry
umbrella morph
undulating tangle
undulating undulations
untangle
volatile
watershed
wavy circlet
whatsit
wispy with white zigzags
wow
wrapping
wrought copper spirograph
yawn
yellow and red flower
yellow gold curve
yellow orange rounded square waves
yellow whirlygig
zigzaggy colourful flower