When we use the wolframalpha to plot a complex function, like
$$f \left( z \right) = e^z, \text{ } z \in \mathbb{C}$$
, the program show us the conformal map, that take vertical and horizontal lines from
$$z = a + bi = (a,b) \in \mathbb{R}^2 \cong \mathbb{C}$$
to
$$f \left( z \right) = e^z = e^{a + bi} = c + di = (c,d) \in \mathbb{R}^2 \cong \mathbb{C}$$.
Now, imagine a quaternion function like
$$f \left( q \right) = e^{q}, \text{ } q \in \mathbb{H}$$ $$f \left( a_1 + b_1 i + c_1 j + d_1 k \right) = e^{a_1 + b_1 i + c_1 j + d_1 k} = a_2 + b_2 i + c_2 j + d_2 k$$
My question: there is a program, software, site or anything, that we can see the conformal map of quaternions, like:
$$(a_1 , b_1) \to (a_2 , b_2)$$
or
$$(a_1,c_1) \to (b_2 , d_2)$$
or
$$(b_1,d_1) \to (a_2,d_2)$$
It would be a nice thing to see, i think. And this concept can be extended to $\mathbb{O}$.
