Two perpendicular oscillations at whole-number frequencies weave a closed ribbon, and the phase between them drifts so the knot keeps retying itself.
Category
Curve & Field Backgrounds
Parametric curves and wave fields drawn straight from their own equations.
22 curve & field backgrounds
A small wheel rolls inside a larger one and the pen offset slides in and out, so the rosette opens and closes without ever breaking its loop.
Rose Curve
10sA single polar equation sweeps a petal at a time around the centre, and the phase rotation walks the petals round without the shape ever changing size.
One polar equation with seven numbers walks from a rounded blob to a spiked star and back, drawing whatever shape lies between them on the way.
Sand settles along the still lines of a vibrating plate, and as the driving mode swings through zero the whole nodal figure inverts and reforms.
Several ripple sources push against each other and the bright bands fall where their crests agree, sliding as the sources beat in and out of phase.
A two line iterated map is run tens of thousands of times and the points pile up into a fractal cloud that never quite crosses its own path.
Flow Field
15sEvery point in the frame is given a direction by a drifting noise field, and hundreds of short streamlines follow whatever direction they land on.
Seeds are placed one golden angle apart on a widening spiral, the arrangement a sunflower head uses, and the whole disc turns and breathes.
A chain of circles each turn on the rim of the one before, and the pen at the end of the chain traces the closed figure their speeds add up to.
Straight chords join every point to a multiple of itself, and the curve you end up seeing is the envelope none of the lines actually traces.
Maurer Rose
12sChords cut straight across a rose curve at a fixed angular step, folding the smooth petals into a faceted star nobody plotted directly.
A trunk splits, and splits again, each fork seeded to lean its own way so the canopy fills in branch by branch and never twice the same.
Six trunks leave the centre at once and branch outward together, so the frame fills from the middle in a single symmetrical burst.
Every edge sprouts a smaller spike on every pass, and the outline draws itself around until the snowflake closes on its own start.
One strip folded in half over and over, never crossing itself, tiling the plane into a shape that looks designed but is only folding.
A single unbroken line finds its way through every cell of the grid exactly once, and you watch it fill the square as it goes.
One continuous path that never lifts or crosses, yet the triangle-inside-a-triangle of Sierpinski appears as the line finishes.
Equal circles laid on a hexagonal grid overlap into the old six-fold rosette, revealed one ring at a time from the centre out.
The lattice appears first, then straight lines connect every neighbouring centre, drawing the lattice's own hidden skeleton over it.
A single closed curve winds through a doughnut it never draws, turning slowly so the strands pass in front of and behind each other.
Two pendulums swing out of step and slowly lose energy, so the trace spirals inward and the figure tightens instead of closing.
What is a parametric curve background?
It is a background drawn from an equation rather than a filter. A Lissajous figure, a spirograph rosette or a Chladni plate is defined by a handful of numbers, so changing one parameter changes the whole shape while the motion stays smooth and loops exactly.
These are the backgrounds you cannot drag an effect onto. Each preset evaluates its own equation every frame, which is why the curves stay sharp at any resolution and why the loop closes rather than cross-fading.
Read the full guide: How to Animate Spirograph and Math Curve BackgroundsFrequently asked
How many curve & field backgrounds does velements have?
22 editable presets, including Lissajous Trace, Spirograph Bloom, Rose Curve, Superformula Morph, Chladni Plate and Wave Interference. Every one opens in the browser editor, where you change colors, timing and any text before you download.
Do these curve & field backgrounds loop?
All 22 loop seamlessly, so you can repeat any of them on your timeline for as long as the shot needs.
Which formats can you export curve & field backgrounds in?
MP4 for any editor or platform, WebM with a transparent background for the web, and a PNG sequence with alpha for Premiere Pro, After Effects, DaVinci Resolve and Figma. Every preset exports in 16:9, 9:16, 1:1 and 4:5 from 720p up to 8K, with a commercial license in your name.
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