Custom equation

Custom Equations — type your own system. The Equations module takes dx/dt, dy/dt and dz/dt (plus dw/dt for a 4-D system) as text and integrates them with forward Euler, the same way the classic attractors are stepped. The iterate switch reads the same expressions as a discrete MAP instead — x = f(x,y,z) rather than x += dt·f(x,y,z) — which has no dt and no path between iterates, so it draws as a cloud of points the way Henon and Ikeda do.

There is no eval: expressions are tokenized, converted to RPN and interpreted over a small value stack, so nothing but arithmetic can run. Grammar is + − × ÷ ^ with grouping and implicit multiplication (2x, 3(x+1)), the functions sin cos tan asin acos atan exp log ln sqrt abs sign sinh cosh tanh floor, the constants pi e tau, and the variables x y z w t. Any other name becomes a free parameter and is auto-exposed as its own knob.

Open Custom equation in chaosrack →

It opens running, on the model selector, with its own knobs. Rotate it by dragging, zoom with the wheel, and turn the parameters to see what the figure does when the system changes.