System Functions : Complex Functions
Unlike trajecvtory Curves, this graph considers the course of complex functions on real and imaginary axes.
Unlike other graphs, the settings and graph are located in the same window.
Only functions containing the variables z and param are permitted. Alternatively, the variables x and y can be used as shorthand for the real and imaginary parts. Enter the desired function in the input field for the function, or select one of the existing functions by clicking on the arrow to the right of the input field.
CGRAPH plots the complex result values of the functions on the real and imaginary axes within the value range for the variable z. Complex numbers are permitted for both z and the parameter.
After clicking the Create graph button, CGRAPH displays the graph.
The default values can be viewed in the tree on the left. Clicking on the (optional) parameter also unlocks the parameter's adjustability in the complex plane. An explanation of this function can be found in the notes on changing the parameter in the graph display. The parameter can also be restricted to purely real values.
The example shows a function that returns the numbers of the Fibonacci sequence as zero points for a parameter tau (golden ratio = 1.6180339887…). However, if you vary the parameter, the display changes completely.
The values can be changed retrospectively. The graphic is adjusted automatically, at the latest when the Create graphic button is clicked. Clicking on the coloured symbol for the function, etc. allows you to quickly hide the graphic from the display. Double-clicking on the text allows you to adjust the graphical representation.
The display of the axes is also part of the tree, as the graphics for this graphic type are independent of each other and can be set separately.