🌹 Polar Equation Plotter

In polar coordinates a point is described by (r, θ) — its distance r from the origin and the angle θ it makes with the positive x-axis — instead of the familiar (x, y). Many curves that look messy in x/y become simple in polar form, because a polar equation r = f(θ) directly says how far the curve reaches at each angle. This makes circles, spirals and flower-like shapes natural to express and easy to draw.

A rose r = cos(kθ) draws petals — k petals when k is odd and 2k when k is even. A cardioid r = 1 − cos θ traces a heart shape. A lemniscate forms a figure-eight, and the Archimedean spiral r = θ winds outward at a steady rate as the angle grows. Each preset in this plotter loads one of these classic equations so you can see the whole family and then tweak the numbers to make your own variations.

Your expression is read by a custom whitelist math parser — not JavaScript eval — so only the listed functions (sin, cos, tan, sqrt, abs, exp, log, pow), the constants pi and e, and the variable theta are accepted; anything else is rejected before it can run. The theta range controls how much of the curve is swept out (a full flower usually needs 0 to 2π or more), and the scale control zooms the drawing so tall or tiny curves fit the canvas.