Dancing in a Circle
Simulates four equal masses chasing one another on a shared circular path — a periodic four-body choreography that returns to its starting arrangement instead of flying apart.
Scenarios
Choreographies
Periodic solutions to the gravitational n-body problem: equal masses tracing the same closed curve, offset in phase, so the pattern repeats forever. From the Chenciner–Montgomery figure-eight to pentagrams, hexagons, and the Star of David — mathematically exact orbital dances with no central star.
Four Corners
Simulates a five-body choreography with four masses at the corners of a square, each on a small elliptical loop, while a fifth body keeps the periodic square from collapsing.
Hexagon
Simulates four equal masses whose paths outline a hexagon. After one cycle every body returns to its start — a periodic four-body solution whose six-fold figure is gravity alone.
Pentagram
Simulates five equal masses tracing a pentagram as they orbit one another. The five-pointed star is a periodic n-body solution: the system repeats after one complete cycle.
Square Within a Circle
Simulates four equal masses whose paths form a square rotating inside a circle. No central body anchors the motion — the pattern comes from mutual Newtonian gravity alone.
The All Seeing Eye
Simulates four equal masses whose overlapping paths draw an almond-shaped eye with a central focus. The periodic four-body solution has no central star; the shape is gravity alone.
The Figure Eight N-body Choreography
Simulates the Chenciner–Montgomery figure-eight: three equal masses tracing one closed curve, each offset by a third of a period, repeating forever under Newtonian gravity.
The Sleeping Snow Man
Simulates three equal masses on a choreography shaped like a sleeping snowman: two stacked loops with a smaller head. Each mass traces the same curve, offset in phase from the others.
The Star of David N-body Choreography
Simulates six equal masses tracing a Star of David — two overlapping triangles. Each body follows the same closed curve, offset by one-sixth of a period from its neighbors.
Triangle
Simulates four masses in a triangular choreography: three bodies loop at the vertices while a fourth completes the periodic pattern, combining triangular symmetry with small ellipses.
X Marks the Spot
Simulates three equal masses whose paths cross at the center to draw an X inside a circle. Each body passes through the same central region at different times of the periodic cycle.