The catalog

147 motifs in 19 families, as of geomotif 1.3.1. Every one of them resamples by arc length, takes every spacing curve, and exports to SVG, DXF, GIF, CSV, TXT, JSON and a spec file.

The pictures are in the gallery; this page is the same list in a form you can search and read.

curve

Motif	Class	Summary
astroid	Astroid	The four-cusped star x**(2/3) + y**(2/3) == 1.
bow	BowCurve	The bow, x**4 == x**2*y - y**3: two loops pinched at the origin.
butterfly	Butterfly	Temple Fay's butterfly: twelve revolutions that draw two wings.
cardioid	Cardioid	The heart-shaped r = 1 + cos(theta): one circle rolled around another.
cassini-oval	CassiniOval	Points whose distances to two foci multiply to a constant.
cochleoid	Cochleoid	The snail shell r = sin(theta) / theta, coiling in on itself.
cornoid	Cornoid	The cornoid, x = cos(t)cos(2t), y = sin(t)(2 + cos(2t)).
cycloid	Cycloid	The path of a point on a rolling wheel's rim.
deltoid	Deltoid	The three-cusped tricuspoid, Euler's curve of 1745.
fish	FishCurve	A fish, tail and all, from x = cos(t) - sin(t)**2 / sqrt(2).
folium	Folium	The leaf curve r = cos(theta) * (4*a*sin(theta)**2 - b).
heart	Heart	A heart, in either of the two shapes that go by the name.
lemniscate	Lemniscate	Bernoulli's lemniscate: the infinity symbol.
lemniscate.gerono	LemniscateOfGerono	Gerono's lemniscate: the other figure eight, x**4 = x**2 - y**2.
limacon	Limacon	Pascal's snail, r = b + a*cos(theta), inner loop and all.
nephroid	Nephroid	The kidney: the two-cusped epicycloid, r = 3cos(t) - cos(3t).
trochoid	Trochoid	The path of a point fixed to a rolling wheel, on the rim or off it.
witch-of-agnesi	Witch	The witch of Agnesi: a bell curve with an exact algebraic definition.

fractal

Motif	Class	Summary
fractal.apollonian	ApollonianGasket	Circles packed into circles, filling every gap they leave.
fractal.cantor	CantorSet	Take out the middle third. Repeat. Stack the rounds to see it happen.
fractal.dragon	DragonCurve	The Heighway dragon: fold a strip of paper in half, repeatedly, unfold.
fractal.gosper	GosperCurve	The flowsnake: a space-filling curve on a hexagonal grid.
fractal.h-tree	HTree	An H whose serifs are smaller H's, and so on down.
fractal.hilbert	HilbertCurve	The space-filling curve that keeps neighbours together.
fractal.koch	KochCurve	The original: replace the middle third of every segment with a spike.
fractal.koch-antisnowflake	KochAntisnowflake	The snowflake with its spikes turned inward, which is a different shape.
fractal.koch-snowflake	KochSnowflake	Three Koch curves around a triangle: finite area, infinite perimeter.
fractal.levy-c	LevyCCurve	Paul Levy's C curve: two half-size copies at right angles, forever.
fractal.minkowski	MinkowskiSausage	Koch's idea on a square grid: a battlement instead of a spike.
fractal.minkowski-island	MinkowskiIsland	Four Minkowski sausages around a square: the quadratic Koch island.
fractal.moore	MooreCurve	Hilbert's curve closed into a loop.
fractal.peano	PeanoCurve	The first space-filling curve ever published, from 1890.
fractal.pythagoras-tree	PythagorasTree	Squares on the legs of right triangles, all the way up.
fractal.sierpinski-arrowhead	SierpinskiArrowhead	The gasket approached along a curve instead of through a triangle.
fractal.sierpinski-carpet	SierpinskiCarpet	A square with its middle ninth removed, then again in each ninth.
fractal.sierpinski-triangle	SierpinskiTriangle	The gasket, drawn as one unbroken stroke that closes on itself.
fractal.terdragon	Terdragon	The dragon done in thirds: one segment becomes three at 120 degrees.
fractal.twindragon	TwinDragon	Two Heighway dragons back to back, enclosing a region that tiles.
fractal.vicsek	VicsekFractal	The box fractal: a plus sign made of plus signs.
points.barnsley-fern	BarnsleyFern	Four affine maps and a coin, producing a fern.
points.ifs	IFSAttractor	The chaos game: pick a map at random, apply it, plot the point, repeat.

girih

Motif	Class	Summary
girih.hex-star	HexStarLattice	Six-pointed stars on a triangular lattice, rhombi filling the gaps.
girih.interlocking-decagons	InterlockingDecagons	The pattern the tenfold tiling carries: ten-pointed stars, interlocked.
girih.rosette	Rosette	The shamsa: a star, a blunter star inside it, and so on inward.
girih.rosette-tiling	RosetteTiling	A field of rosettes, touching point to point.
girih.tenfold	TenfoldGirih	Regular decagons laid edge to edge, with a bowtie in every gap.
girih.tile	GirihTile	One of the five girih tiles, with the strapwork it carries.

graph

Motif	Class	Summary
graph.bipartite	BipartiteGraph	Two rows of nodes, and every line from one row to the other.
graph.chord	ChordDiagram	Nodes on a circle and whichever chords you name between them.
graph.complete	CompleteGraph	Every node joined to every other: K5, K12, and the ones in between.
graph.cyclic	CyclicGraph	The circulant: join every node to the ones a fixed number of steps away.
graph.prime-chords	PrimeChords	Join two numbers whenever they add up to a prime.
modular.addition	ModularAddition	Join each number to the one a fixed distance further round.
modular.multiplication	ModularMultiplication	The times table drawn as chords, which turns out to be a cardioid.

guilloche

Motif	Class	Summary
guilloche.band	GuillocheBand	A woven ribbon along a straight spine: the border of a banknote.
guilloche.pattern	GuillochePattern	A rosette inside a woven border, with rules between: the banknote layout.
guilloche.rosette	GuillocheRosette	A stack of rosettes, each turned a little further than the last.

harmonic

Motif	Class	Summary
harmonic	Harmonic	Sums of sines on each axis: Lissajous with more terms.
harmonograph	Harmonograph	The Victorian drawing machine: swinging pendulums, slowly running down.
lissajous	Lissajous	Two perpendicular oscillations, plotted against each other.

illusion

Motif	Class	Summary
illusion.cafe-wall	CafeWall	Parallel mortar lines that refuse to look parallel.
illusion.impossible-cube	ImpossibleCube	The same cube, told two contradictory things about which face is nearer.
illusion.moire	MoirePattern	Two regular patterns laid over each other, and the fringes between them.
illusion.necker-cube	NeckerCube	A wireframe cube with nothing to say which face is in front.
illusion.penrose-stairs	PenroseStairs	The endless staircase: four flights, every step up, back where you began.
illusion.penrose-triangle	PenroseTriangle	The tribar: three square beams meeting at three right angles.

knot

Motif	Class	Summary
knot.celtic-grid	CelticGrid	The plait: strands at 45 degrees, bouncing off the frame and off barriers.
knot.circular	CircularCelticKnot	One strand wound several times round a ring, weaving with itself.
knot.endless	EndlessKnot	The endless knot: four strands each way, woven, with their ends looped back.
knot.square	SquareCelticKnot	The same winding, but round a square frame instead of a ring.
knot.triquetra	Triquetra	The trinity knot: three arcs that turn out to be one strand.

mandala

Motif	Class	Summary
kaleidoscope	Kaleidoscope	One motif, repeated under a cyclic or dihedral symmetry group.
layered-rings	LayeredRings	Concentric circles: the other half of a mandala's scaffolding.
mandala	Mandala	Concentric rings of repeated motifs.
snowflake	Snowflake	Six identical arms, each mirrored in its own axis.
spoke-pattern	SpokePattern	Radial lines from an inner circle to an outer one.

polar

Motif	Class	Summary
points.phyllotaxis	Phyllotaxis	The sunflower head: r = c*sqrt(n) at n golden angles.
polar.expression	PolarExpression	Any radius function you like, wrapped as a motif.
rose	Rose	The rhodonea r = cos(n/d * theta), with the petal count right.
rose.maurer	MaurerRose	A rose walked in whole-degree steps and joined by straight chords.

primitive

Motif	Class	Summary
arc	Arc	Part of a circle: sweep radians of it, starting at start_angle.
circle	Circle	A circle of radius radius around center.
egg	Egg	An oval fatter at one end than the other.
ellipse	Ellipse	An ellipse with semi-axes rx and ry, optionally rotated.
line	Line	A straight segment from start to end.
points.grid	PointGrid	A rectangular lattice of loose points, optionally staggered.
points.poisson	PoissonDiscPoints	Points scattered at random, but never closer together than a set distance.
polygon.regular	RegularPolygon	A regular sides-gon inscribed in a circle of radius radius.
polygon.reuleaux	ReuleauxPolygon	A curve of constant width: the Reuleaux triangle and its odd-sided kin.
polygon.star	StarPolygon	The {n/k} star polygon: every step-th corner of an n-gon.
rectangle	Rectangle	An axis-aligned rectangle centered on center.
rectangle.rounded	RoundedRectangle	A rectangle with its corners replaced by quarter circles.
sector	Sector	A pie slice: an arc closed back to its center by two radii.
squircle	Squircle	The square-circle midpoint: a Superellipse with n = 4.
star	Star	The star people actually draw: outer points joined through inner ones.
superellipse	Superellipse	The curve \|x/rx\|**n + \|y/ry\|**n == 1, for any positive n.

roulette

Motif	Class	Summary
epicycles	Epicycles	Rotating arms stacked tip to tail; the path of the last tip.
roulette.epicycloid	Epicycloid	A point on the rim of a wheel rolling outside a ring: a ring of petals.
roulette.epitrochoid	Epitrochoid	A pen fixed to a wheel rolling around the outside of a ring.
roulette.hypocycloid	Hypocycloid	A point on the rim of a wheel rolling inside a ring: a cusped star.
roulette.hypotrochoid	Hypotrochoid	A pen fixed to a wheel rolling around the inside of a ring.
spirograph	Spirograph	The toy, in the toy's own terms: a ring, a wheel and a hole.

sacred

Motif	Class	Summary
sacred.flower-of-life	FlowerOfLife	The seed of life continued outward: circles on a hexagonal grid.
sacred.fruit-of-life	FruitOfLife	The thirteen circles of the flower that touch without overlapping.
sacred.golden-rectangle	GoldenRectangle	A rectangle that keeps its shape when you cut a square off it.
sacred.metatrons-cube	MetatronsCube	Thirteen circles with every pair of middles joined by a line.
sacred.seed-of-life	SeedOfLife	Seven circles: one in the middle, six around it, all the same size.
sacred.sri-yantra	SriYantra	Nine interlocking triangles inside a circle, four pointing up and five down.
sacred.vesica	VesicaPiscis	Two circles, each through the other's middle.

solid

Motif	Class	Summary
solid.cube	Cube	Six squares. Dual to the octahedron, and the one everybody can check.
solid.dodecahedron	Dodecahedron	Twelve pentagons, built on a cube and the golden ratio.
solid.icosahedron	Icosahedron	Twenty triangles: three golden rectangles at right angles to each other.
solid.octahedron	Octahedron	Eight triangles: a corner of the cube's every face, joined up.
solid.polyhedron	Polyhedron	Any solid you like: your corners, your edges.
solid.tetrahedron	Tetrahedron	Four triangles: the simplest solid there is, and its own dual.
solid.truncated-icosahedron	TruncatedIcosahedron	The football: twelve pentagons and twenty hexagons.

spiral

Motif	Class	Summary
spiral.archimedean	ArchimedeanSpiral	The arithmetic spiral r = a + b*theta.
spiral.between	SpiralBetween	The endpoint-constrained arithmetic spiral: r = a + b*theta.
spiral.euler	EulerSpiral	The clothoid: curvature increasing linearly with distance traveled.
spiral.fermat	FermatSpiral	The parabolic spiral r = a * sqrt(theta), both branches.
spiral.fibonacci	FibonacciSpiral	Quarter circles inscribed in a chain of Fibonacci squares.
spiral.golden	GoldenSpiral	The logarithmic spiral that widens by the golden ratio each quarter turn.
spiral.hyperbolic	HyperbolicSpiral	The reciprocal spiral r = a / theta.
spiral.involute	CircleInvolute	The path of a string unwinding, taut, from a circle.
spiral.lituus	Lituus	The spiral r = a / sqrt(theta), named for the Roman augur's staff.
spiral.logarithmic	LogarithmicSpiral	The equiangular spiral r = a * exp(b*theta).
spiral.theodorus	TheodorusSpiral	The square-root spiral: a chain of right triangles, drawn exactly.

string-art

Motif	Class	Summary
string-art.corner	StringArtCorner	Two arms, laced so the far end of one meets the near end of the other.
string-art.envelope	StringArtEnvelope	The general engine: nail i on one curve, to nail rule(i) on another.
string-art.polygon	StringArtPolygon	A strung corner at every corner of a regular polygon.

symmetry

Motif	Class	Summary
symmetry.point-set	SymmetricPointSet	Points arranged by a symmetry group, spaced by iterative relaxation.

tiling

Motif	Class	Summary
tiling.ammann-beenker	AmmannBeenker	The octagonal quasicrystal: squares and 45-degree rhombs, never repeating.
tiling.cairo	CairoPentagonal	The Cairo tiling: pentagons in fours, spinning like a pinwheel.
tiling.herringbone	HerringboneTiling	Rectangles laid in chevrons, each one's end against the next one's side.
tiling.hexagonal	HexagonalTiling	The honeycomb: regular hexagons, three to a corner.
tiling.penrose-p2	PenroseP2	Penrose's kite and dart, the tiling that cannot repeat.
tiling.penrose-p3	PenroseP3	Penrose's rhombs: one thin, one thick, and no repeating pattern ever.
tiling.rhombille	RhombilleTiling	Tumbling blocks: each hexagon split into three rhombi.
tiling.snub-square	SnubSquare	Squares and triangles, two of each at every corner -- the 3.3.4.3.4.
tiling.square	SquareTiling	Squares edge to edge: the graph paper of tilings.
tiling.triangular	TriangularTiling	Equilateral triangles, alternately point up and point down.
tiling.truchet	TruchetTiling	Quarter-circles in square cells, each turned at random.
tiling.truncated-square	TruncatedSquare	Octagons with small squares in the gaps -- the 4.8.8 tiling.

voronoi

Motif	Class	Summary
voronoi.cells	VoronoiCells	The same map, drawn one closed region at a time.
voronoi.delaunay	Delaunay	The triangulation that joins points whose Voronoi cells touch.
voronoi.diagram	Voronoi	The map of which point is nearest, drawn as its borders.
voronoi.lloyd	LloydRelaxation	Points nudged toward the middle of their own cells, over and over.