Modes and Options


The system being graphed is the one with the current tab open. So if Complex Plane is open then the dynamical system uses the z = ... equation and it is graphed on the complex plane. If the Real Plane tab is open then it will graph x = ... and y = ... parametric equations. The syntax and available functions for the program are on the Expression Syntax page.

The Complex Plane tab has two modes of operation, Fix z and Fix c. In the Fix z mode the initial z value is given on that line and used in the first iteration of the dynamical system, z = .... After that, the subsequent values of z are fed back into the system. The value of c is taken from each point (pixel) in the complex plane image and is held constant through the dynamical system for that point. This can be thought of as Mandelbrot mode for the system since with this option and the formula z = z^2 + c, one will get the Mandelbrot set.

In the Fix c mode the value of c is held constant for each point (pixel) in the complex plane and the initial value of z is taken from each point (pixel) in the complex plane image. This can be thought of as Julia set mode for the system since with this option and the formula z = z^2 + c, one will get the Julia set associated with the complex number c.

The Real Plane tab has the equivalent options for the real plane. The Fix (x, y) mode is a Mandelbrot mode with the initial value of (x, y) taken from the panel and the (c, d) values range over the plane. The Fix (c, d) mode is a Julia set mode where the values of (c, d) are fixed throughout the generation of the image and the initial values of (x, y) are taken from the plane.

The other options apply to both types of systems.