Image smoothing and edge preservation

Type any function and see its shape straight away. Plot up to three at once in three colours to compare them, drag the trace point to read a value off a curve, and see where each one crosses zero.

Move m and watch the line tilt; move b and watch it slide. Or drag the two points on the line and read the equation it writes back. A rise-over-run staircase climbs the line so slope becomes something you can count.

Two bodies under gravity trace an ellipse forever and you can write the formula down. Add a third and no such formula exists. Run the figure-eight orbit, nudge one mass, and watch a stable pattern become unpredictable while the total energy stays put.

Approximate the area under a curve with strips and choose how each takes its height: left edge, right edge, middle, or a sloping top. Push the strip count up and watch the error fall, with the running total plotted as its own curve.

Two paths start a hair apart and follow the same three equations. Watch them agree, then part onto opposite wings of the butterfly. Drag the start, spin the shape and pull rho down until chaos stops.