Parametric Geometry · One hundred studies

Lines under tension

One hundred stroke-built systems. Each drawing is recalculated from a single spring value. Move across the field to disturb the geometry.

ƒ(t, parameters) → svg
0016 × 6 / circles

Overlap field

0027 × 7 / cells

Diagonal fall

0039 + 12 / curves

Axial horn

0043 : 2 / resonance

Orbital ratio

0057 / hypotrochoids

Rolling point

00615 / harmonics

Phase weather

0075 to 6 / lobes

Petal exchange

0089 × 9 / geodesics

Saddle measure

00984 / seeds

Golden drift

0103 / trajectories

Strange orbit

0117 + 16 / rulings

Half-twist

012(2, 3) / knot

Braided torus

013epicycloid / nested / v1

Crown orbit

014epicycloid / nested / v2

Sevenfold wheel

015epicycloid / nested / v3

Cusped transit

016epicycloid / nested / v4

Satellite bloom

017superformula / layers / v1

Lamé weather

018superformula / layers / v2

Soft symmetry

019superformula / layers / v3

Polygon tide

020superformula / layers / v4

Exponent bloom

021r = √θ / arms / v1

Root spiral

022r = √θ / arms / v2

Fermat fan

023r = √θ / arms / v3

Radical drift

024r = √θ / arms / v4

Square-root field

02512 / Archimedean / v1

Coiled current

02612 / Archimedean / v2

Twelve winds

02712 / Archimedean / v3

Vortex sheaf

02812 / Archimedean / v4

Spiral aperture

029exp(cos θ) / trace / v1

Butterfly trace

030exp(cos θ) / trace / v2

Exponential wings

031exp(cos θ) / trace / v3

Oscillating moth

032exp(cos θ) / trace / v4

Fourfold flight

03315 / wave sums / v1

Fourier veil

03415 / wave sums / v2

Partial chorus

03515 / wave sums / v3

Harmonic cloth

03615 / wave sums / v4

Spectral ribbon

037modular chords / rose / v1

Maurer crossing

038modular chords / rose / v2

Modular rose

039modular chords / rose / v3

Degree walk

040modular chords / rose / v4

Petal arithmetic

041n × k mod n / v1

Times table

042n × k mod n / v2

Circular product

043n × k mod n / v3

Modular web

044n × k mod n / v4

Chord arithmetic

0457 × 7 / arc field / v1

Truchet current

0467 × 7 / arc field / v2

Binary meander

0477 × 7 / arc field / v3

Arc grammar

0487 × 7 / arc field / v4

Tiled passage

049tangent ring system / v1

Tangent choir

050tangent ring system / v2

Orbit bubbles

051tangent ring system / v3

Contact system

052tangent ring system / v4

Apollonian echo

053r = aeᵇθ / 8 arms / v1

Logarithmic wind

054r = aeᵇθ / 8 arms / v2

Golden curl

055r = aeᵇθ / 8 arms / v3

Equiangular arms

056r = aeᵇθ / 8 arms / v4

Growth spiral

05715 / linked waves / v1

Kinematic chain

05815 / linked waves / v2

Linked phase

05915 / linked waves / v3

Joint cascade

06015 / linked waves / v4

Serial motion

061loxodrome / projection / v1

Rhumb sphere

062loxodrome / projection / v2

Constant bearing

063loxodrome / projection / v3

Loxodromic globe

064loxodrome / projection / v4

Poleward course

065Klein surface / slices / v1

Klein sections

066Klein surface / slices / v2

Bottle rulings

067Klein surface / slices / v3

Immersed loop

068Klein surface / slices / v4

Nonorientable skin

069Fourier heart / 7 / v1

Cardioid score

070Fourier heart / 7 / v2

Pulse equation

071Fourier heart / 7 / v3

Harmonic chamber

072Fourier heart / 7 / v4

Four-term heart

073Bessel-like / 13 / v1

Bessel membrane

074Bessel-like / 13 / v2

Radial zeroes

075Bessel-like / 13 / v3

Damped chorus

076Bessel-like / 13 / v4

Cylindrical wave

077Tₙ(x) / 11 / v1

Chebyshev loom

078Tₙ(x) / 11 / v2

Extremal bands

079Tₙ(x) / 11 / v3

Cosine polynomial

080Tₙ(x) / 11 / v4

Minimax field

081circle envelope / chords / v1

Coffee caustic

082circle envelope / chords / v2

Envelope light

083circle envelope / chords / v3

Catacaustic fan

084circle envelope / chords / v4

Reflected focus

085constant-width / rings / v1

Reuleaux orbit

086constant-width / rings / v2

Constant width

087constant-width / rings / v3

Curved triangle

088constant-width / rings / v4

Rotor constellation

089roulette / nested / v1

Epitrochoid lace

090roulette / nested / v2

Outer roulette

091roulette / nested / v3

Rolling halo

092roulette / nested / v4

Trochoid crown

093Clifford map / 7 / v1

Clifford weather

094Clifford map / 7 / v2

Strange basin

095Clifford map / 7 / v3

Iterated climate

096Clifford map / 7 / v4

Attractor threads

097(p, q) / strands / v1

Harmonic knot

098(p, q) / strands / v2

Frequency braid

099(p, q) / strands / v3

Lissajous knot

100(p, q) / strands / v4

Resonant tangle

View