Complex Dynamics Visualization Tool

Parameter Space






Dynamical Plane






General information

  • This Javascript applet generates a plot of parameter space associated to the complex function f(z,c), and renders a plot of the dynamical plane associated to the chosen value of the parameter "c".
  • Points are colored according to their escape time, which is the number of iterations of f(z,c) required for escape(z,c) to return true.
  • The white point in the parameter space corresponds to the value of "c" for the dynamical plane. This point is draggable, with the plot of the dynamical plane updating in real time.
  • The white point in the dynamical plane is the starting point for a plot of the first 8 iterates. This can also be dragged.
  • The use of GPU acceleration limits accuracy beyond a certain level of zoom.

Controls

  • The plot window can be moved via either the arrow keys or by clicking and dragging.
  • The zoom level may be adjusted via the +/- keys.
  • The white point in each plot may be clicked and dragged to change its value.
  • Press "enter" to apply changes.

Predefined objects

  • Constants: e, pi, i.
  • Operations: z*w, z^w, z+w, z-w, z/w, |z|, sqrt, exp, log, sin, cos, tan, arcsin, arccos, arctan, arctan2(x,y), lambertw, re, im, conjugate, arg, mod(x,y), round, floor, ceil.
  • Misc. functions: random(x) (random float in (0,x)), randomint(n) (random integer in [0,n]), randombool() (random true/false).