how to use wolfram mathematica phase portraits

I winged the color function a bit.Cite this as: Wolfram Research (1991), Contours, Wolfram Language function, (updated 2007). Of course, Michael Trott wrote the Mathematica guide books, which contain many beautiful graphics, but seem to have fallen behind the accelerated Mathematica release schedule! The Return of Riemann surfaces (updates for Mma v6) Visualizing Riemann surfaces of algebraic functions, IIa, IIb, IIc, IId. Not that this should stop you from giving your favourite approach that uses a lower level construction!Įdit: There were some nice articles by Michael Trott in the Mathematica journal on: I know that there are other ways to visualize complex functions - such as the 'neat example' in the Plot3D docs, but that's not what I want.Īlso, I do have one solution below (that has actually been used to generate some graphics used in Wikipedia), but it defines a fairly low level function, and I think that it should be possible with a high level function like ContourPlot or DensityPlot. Note that this is not a problem with Plot3D where all 3 parameters (x,y,z) get passed to ColorFunction. But the problem is in both types of plots, ColorFunction only takes a single variable equal to the contour or density at the point - so it seems impossible to make it colour the phase/argument while plotting the absolute value. In the Mathematica documentation page Functions Of Complex Variables it says that you can visualize complex functions using ContourPlot and DensityPlot 'potentially coloring by phase'. Hampton of Neutral Drifts) of the zeta function with overlayed contours of absolute value: How can I make a Mathematica graphics that copies the behaviour of complex_plot in sage? i.e.

How to use wolfram mathematica phase portraits