x[n+1]=c*x[n]*(1-x[n])where n denotes the discrete time steps and x is the quantity changing over time. If time is measured continuously, the resulting continuous dynamical systems are expressed as ordinary differential equations, for instance
dx/dt = c*x*(1-x)where x is the quantity that changes with time t. Here we will consider only discrete dynamical systems.
This may seem very complex, but from the point of view of the computer graphics programmer, it is very simple. In the end you have a formula that for a system described by two variables,like a pendulum in the plane, is a planar discrete system of the form:
x = f(x,y) y = g(x,y)When this formula is iterated starting from some initial point x0,y0 you are in fact solving numerically a differential equation, describing the behavior in time, of some physical system, like a pendulum, where x and y may be the space s along the trajectory and the speed v.