logistic map

In issue 29 of Plus, we heard how a simple mathematical equation became the subject of a debate in the UK parliament. Chris Budd and Chris Sangwin continue the story of the mighty quadratic equation.

Tags: bernoulli equation : navier-stokes equations : gravity : ellipse : chaos : differential equation : public understanding of mathematics : quadratic equation : circle : parabola : hyperbola : acceleration : stopping time : galileo : Newton : pendulum : Euler : complex number : logistic map : copernicus : kepler

Images based on Lyapunov Exponent fractals are very striking. Andy Burbanks explains what Lyapunov Exponents are, what the much misunderstood phenomenon of chaos really is, and how you can iterate functions to produce marvellous images of chaos from simple mathematics.

Tags: mathematics and art : fractal : chaos : dynamical system : logistic map : iteration : error : Lyapunov Exponent : orbit : bifurcation