Click on the green flag and watch. Run in Turbo mode.
See page 141 of Chaos: Making a New Science by James Gleick. In 1976 Otto Rössler found a system of three equations that is one of the simplest examples of chaos (deterministic but unpredictable) in a continuous system. The set of equations can be thought of as the laws of motion for a point in three-dimensional space (phase space) with the coordinates (x, y, z). The Rössler attractor is defined by these three equations. x’ = –(y + z) y’ = x + ay z’ = b + xz – cz [a, b, and c are constants, I used a = 0.2, b = 0.2, and c = 5.7] x', y', z' are symbols for dx/dt, dy/dt, and dz/dt. In the code you will see a variable t, representing dt. A particle starting near the origin in the X-Y plane spirals out to the edge and then climbs rapidly in the direction of the Z axis. At some maximum Z-value it dips back down, close to the X-Y plane and begins to spiral until lifted again. This process is repeated indefinitely and the particle always moves to a point it’s never been to. In other words, there is an infinite amount of detail in the attractor.
