On the Scientific Visualization of Complex‐Valued Functions of One Complex Variable

In [1] a method for colour‐map scientific visualization of parametric surfaces in 3D space was proposed. In [1] this method was applied for pixel‐based computation of the solution of geometrical intersection problems in 3D using the computer’s GPU (Graphics Processing Unit, i.e., graphics card) as a computational resource with parallel architecture. In the present work we represent the complex‐valued function w = f(z) of one complex argument as a surface in 3D (with parametrization x1 = φ(u,v), x2 = ψ(u,v), x3 = 0, where u = Rz, v = Sz, φ = Rw, ψ = Sw) and apply the above‐said method of [1]. The resulting approach is illustrated on several graphical examples.In its introduction the paper contains also a concise overview of other known approaches and techniques for scientific visualization of complex‐valued functions of a complex variable.Among some topics for future work, in the final section we discuss the possibility of extending the approach proposed here for visualization of graphs of vector functions...