Here's the Wolfram Mathworld article stating that it is unknown whether the Mandlebrot set is path connected.Ī drag-and-drop demonstration of the orbits on a mandelbrot set. an encyclopedia of features of the Mandelbrot set. Here's an excellent tutorial on the relationship between Mandelbrot and Julia sets, and on how the Fibonacci numbers appear. Interactive animated javascript: use zoom = 920. Interactive animated javascript: use zoom = 860.

Interactive animated javascript: use zoom = 875. Interactive animated javascript: use zoom = 1200. Interactive animated javascript with pause and hold: use zoom = 1000. Interactive animated javascript: use zoom = 1000. Interactive animated javascript: use zoom = 900. The link in each entry to the wolfram alpha plot will give an approximate location, and an approximate Julia set. Pictured are the plotted terms in the sequence, graphed usingĬut and paste the value into interactive animated javascript, with suggested zoom, to see the sequence animated.īelow each picture is a designation of whether the original number is in the Mandelbrot set M or not that is, whether its sequence is bounded or not.

The sequence associated to this number is found by iterating z_(n+1) = (z_n)^2 + c. Send entry suggestions to: Entry EditorĮach entry of this encyclopedia is a complex number c = x+ yi. Almost all the entries are focused on points near a bulb of period 14, attached to the main cardiod. This page is a small collection of complex numbers and the.

Wolframalpha sequence