Complex Function w=F(z) or Z2=F(Z1) Plotter Conformal Mapping Method(version 0.2)

A complex function w=F(z) or Z2=F(Z1) will map points, lines/graphs, or regions 
or other objects in one complex plane (z or Z1=x1+y1i) to another complex plane (w or Z2=x2+y2i).
To describe the mapping characteristics of the Complex Function F(z), 
a simple and straightforward method is to map a set of typical objects in z/Z1 plane to 
w/Z2 plane. 

In this complex function plotter, two typical and simple objects are used:
1. a set of rectangular grid, 
2. contour lines of modulus(cycles) and phase(rays).
They are mapped from the complex plane Z1/z to the complex plane Z2/w.
Click "Run/Re-Run Plotter" button to map the pre-defined z/Z1 object to w/Z2 plane with the pre-defined example complex function.
You can change the example function or input your own function expression/formula.
You can select one of the two typical z/Z1 objects.
After any input change, Click "Run/Re-Run Plotter" button to plot the new/re-defined function mapping.
Use "Move Z1 Plane Object" buttons to move the Z1 object and observe its mapped objects on the Z2 plane.
Because the plotted graphs are auto-scaled and auto-centered on the plotter canvas, 
the Z1 object may seems stationary on the Z1 plane, in fact its coordinate marks are changing.
The plotter provides a set of example functions to demo the formula syntax, click the "select menu" to see and select the examples.
This complex function plotter uses the "mathjs" framework for complex function compilation and evaluation, and supports similar functions as the JavaScript Math library.

  Push "Run/Re-Run Plotter" Button to Start