aldus.nexus

Maths art

Type anything: an equation in t, a number, a word or a date. Equations are drawn as they are; everything else becomes a seed for curves, flow fields and strange attractors.

The numbers

Equations

t runs around the curve and p slowly moves with time, so sin(5t + p) drifts as you watch.

How it works

An equation is read by a small parser built into the page: it turns the text into a tree of plus, times, sin and so on, then works it out for a thousand or more values of t around the circle. Nothing you type is ever run as code, even when it arrives in a shared link. One equation is a polar curve, the radius r at angle t; an x = ...; y = ... pair is a parametric curve.

Anything else, a word, a number or a date, is hashed into a 32-bit seed that picks a style and its numbers: a Lissajous figure (two sine waves at a whole-number ratio), a spirograph (a wheel rolling inside a ring), a rose (r = cos(kt)), a flow field (particles following angles taken from smooth noise) or a Clifford attractor (one point jumping by a simple rule, millions of times). The same text always gives the same art.

Save PNG keeps the frame as you see it, glow and trails included. Save SVG writes the current curve as vector paths, so it stays sharp at any size; flow fields and attractors are clouds of dots, so they are PNG only. Copy link puts the input, style and speed in the address, and the gallery keeps up to 24 favourites with small thumbnails in this browser.

a single line of text holds a whole shape, and the same text always grows the same picture.

x = sin(at + δ), y = sin(bt)Lissajous: closes after one turn when a and b are whole numbers
x = (R − r) cos t + d cos((R − r) t / r)
y = (R − r) sin t − d sin((R − r) t / r)spirograph (hypotrochoid): wheel r inside ring R, pen at d; repeats after r / gcd(R, r) turns
r = cos(k t), k = n / drose: n petals for odd n, 2n for even n when d = 1
x′ = sin(a y) + c cos(a x)
y′ = sin(b x) + d cos(b y)Clifford attractor, iterated from one point