Discovered much later than Julia sets, it is generated by taking the set of all functions f(Z)=Z^2+C, looking at all of the possible C points and their Julia sets, and assigning colors to the points based on whether the Julia set is connected or dust.
An extremely complex fractal that is related to Julia sets in the way that it is constructed and by the fact that it acts as a sort of index to the Julia sets.
Submitted By The Authors The Mandelbrot Set is the set of converging points of a plane when tested with the equation z=z2+c, with varying c values.
a set of complex numbers that has a highly convoluted fractal boundary when plotted; the set of all points in the complex plane that are bounded under a certain mathematical iteration
The mapping of the behaviour of a specific complex formula across space by colour coding the result of each starting point as convergent or divergent, generating a fractal boundary.
The set of complex -values for which the orbit of 0 does not escape under iteration of x2 + c. Equivalently, the Mandelbrot set is the set of -values for which the filled Julia set of x2 + c is a connected set.
A mathematical formula that generates particularly beautiful patterns to infinite depths of resolution.
Complex but structured pattern produced by an equation in which the result is fed back into the equation repeatedly; self-similarity.
The Mandelbrot set is a fractal that has become popular outside of mathematics both for its aesthetic appeal and its complicated structure, arising from a simple definition. This is largely due to the efforts of Benoît Mandelbrot and others, who worked hard to communicate this area of mathematics to the general public.