Domain Scale
Range Scale
Draw Bases
Lipschitz Const
Function
branches
t
Graph
f(z) =
Instructions
Inputing Functions
Complex numbers are represented with 2D vectors.
Therefore, f(z) must return a 2D vector.
To input the complex number x + iy write vec2(x, y)
All real numbers must be written with decimal points
e.g. 2.0 , not 2
Function Reference
i, pi and e can be used as constants
For all complex numbers z,w and real number phi:
ccosh(z) returns cosh(z)
z + w returns z + w
cmult(z, w) returns zw
clog(z, phi) returns Logphi(z)
cexp(z) returns ez
cpow(z, w) returns exp(w Log-pi(z))
cpow(z, w, phi) returns exp(w Logphi(z))
csinh(z) returns sinh(z)
ccosh(z) returns cosh(z)
csin(z) returns sin(z)
ccos(z) returns cos(z)
Function Parameters
Change the list of `branches` on the left-panel.
The function will be rendered once for each branch.
Use parameter `branch` in your function definition
to define different branches of your function.
Use parameter t in function definition
to allow for easy editing of some function property
Interaction
Click and drag on the graph to rotate the "domain plane".
Hold `Ctrl` whilst dragging to rotate the "range plane".
How to Interpret the Graph
In order to see how this interpret the 4D graphs drawn by plotter, we can relate them to the simpler case of 2d graphs of real valued functions.
In the graph of a real function f: R -> R there are 2 axes, corresponding to the domain and range of f.
In order to plot a point on the graph of the real function we can move from the origin x units to the right (along the "domain axis"),
and then from there move f(x) units upwards (along the "range axis").
The 4D graph plotter functions in much the same way, whereas instead of having domain and range axes, for a complex function
g(z): C -> C we have a plane for each z and g(z), which we will call the "domain plane" and "range plane".
The "domain plane" has basis {(cos(a), sin(a))T, (cos(b), sin(b))T} and the range plane has basis {(cos(c), sin(c))T, (cos(d), sin(d))T}.
In order to plot a point on the graph of we can move from the origin to the point z in our "domain plane",
and from there move to the point g(z) in our "range plane". This process is repeated for all the points in a subset of our domain.