TITLE: THREE BODY — a gravity playground
PROMPT: Create 'THREE BODY', a gravity playground canvas: two or three colorful masses orbit and slingshot each other with real Newtonian attraction (semi-implicit Euler), trails fading like light-painting, optional central star. Palette: ink background, warm ember and cool cyan bodies with glow. Presets: binary, figure-eight choreography (approx), chaotic trio. Interactions: drag from any point to spawn a body with aimed velocity (slingshot rubber band), click a body to delete with a pop, mass slider for the next spawn, pause/step, and a trails-clear toggle. Soft ambient drone (WebAudio, optional, gesture-gated) whose pitch follows total kinetic energy. Physics made beautiful.
DESCRIPTION: A Newtonian sandbox on ink: bodies attract with inverse-square gravity (semi-implicit Euler, softened), leaving light-paint trails that fade by adjustable memory. Presets: binary (two suns waltzing with a small wanderer), an approximated Chenciner–Montgomery figure-eight choreography, and a chaotic trio. Drag from empty space to spawn a mass with a dashed rubber-band launch vector (length sets speed); click a body to absorb it with a descending pop; sliders for new-body mass, trail memory, and gravity strength; pause/step/trails-clear; live telemetry (body count, total kinetic energy, stability verdict). Bodies glow in warm ember / cool cyan / violet with radial halos over a static starfield.
TECHNIQUES: softened N-body pairwise integration, trail arrays with length capping and alpha-faded rendering, radial-gradient body glows, pointer rubber-band spawn vectors, figure-eight initial conditions from the Chenciner–Montgomery solution (scaled), WebAudio pitch-sweep pops, live kinetic-energy telemetry.
INTERACTION: Drag to aim-and-spawn bodies; click bodies to delete; presets restart the system; sliders tune mass/trails/gravity; pause and single-step for classroom inspection.