RE: Re: Re: Suggestion: Visualization of complex functions with Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg44905] RE: [mg44899] Re: Re: Suggestion: Visualization of complex functions with Mathematica
- From: "David Park" <djmp at earthlink.net>
- Date: Mon, 8 Dec 2003 02:29:14 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
I'd like to add the ComplexAnalysis package at my web site below:
This package contains complex analysis routines and complex graphics
routines. There are routines that convert the regular 2D Graphics into
equivalent complex forms. For example ComplexLine[{z1,z2,z3...}] takes
complex numbers for the point coordinates. There are routines for producing
one or two panel plots or animations of complex functions. Each panel may be
one of the following plot types.
1) Cartesian/PolarSurface - Plots the surface s[f[z]] where f is a complex
function and s is a real function.
2) Cartesian/PolarCoded3D - Plots the surface s[f[z]] and then puts a
colored contour plot on the surface representing r[f[z]] where s and r are
two real functions.
3) Cartesian/PolarGrid - Basically the ComplexMap routines from Mathematica,
but you can combine multiple grids of different colors.
4) Cartesian/PolarContour - 2D colored contour plots with labeling of all or
selected contours.
5) CodedDensity - A density plot using color to code the complex
information. There is one color function provided that codes modulus and
argument. The user can also write and use his own color routines.
6) ComplexVector - Attaches a scaled vector representing the complex value
to each of a set of points. The user supplies whatever set of points he
wishes. This is also useful with animation on a selected point or points to
trace the behavior of the function on paths in the complex plane.
7) RiemannSphere - Maps any set of graphics primitives, but usually a
complex map grid, through a complex function to the Riemann sphere.
The animations are rotation of 3D surfaces and homotopies between two
complex functions. Other custom animations may also be produced. All of the
plot types also allow the user to add extra graphics primitives to embellish
plots
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
From: Peltio [mailto:peltio at twilight.zone]
To: mathgroup at smc.vnet.net
"Murray Eisenberg" wrote
>What is the correct URLs for the ones listed below: www.kfunigratz.ac.at
>is not being found.
I apologize.
The correct URL (I checked it out now) is
http://www.kfunigraz.ac.at/imawww/vqm/pages/dlgraph.html
While searching the web for the correct address, I've also found the
following packages that can be used to plot complex functions (I'm sure that
there are many more). Some are new to me, but the original poster might find
them interesting enough to try'em out.
They can be reached by using the author name, the package name in Google
(www.google.com) For example fill in the search field with "ComplexPlot.m"
or "complex mathematica filetype:m".
Complex.m by Goeran Andersson
http://www.funet.fi/pub/sci/math/mathematica/Analysis/Complex.m
*zListPlot[ zlist, opts] pointplots the complex numbers in zlist.
*zwPlot[ z, w, {t, tmin, tmax}, opts] plots the complex mapping
w=f(z), z=z(t).
ComplexPlot.m by Jeff Olson
http://www.ph.utexas.edu/~jdolson/math/ComplexPlot.m
*ComplexPlot[func, {fx, fy}, {t, tmin, tmax}]
*ComplexListPlot[{z1, z2, ...}] plots a list of complex numbers.
*ComplexVectorPlot[func, {xmin, xmax}, {ymin, ymax}]
*ComplexPartialPlots[func, {xmin, xmax}, {ymin, ymax}]
*ComplexColorPlot[func, {xmin, xmax}, {ymin, ymax}]
*ComplexContourPlot[func, {xmin, xmax}, {ymin, ymax}]
*CartesianMap[f, {x0, x1, (dx)}, {y0, y1, (dy)}] plots the image
of the cartesian coordinate lines under the function f.
*PolarMap[f, {r0:0, r1, (dr)}, {phi0, phi1, (dphi)}] plots the
image of the polar coordinate lines under the function f.
ComplexPlot3D by Kevin McIsaac
*ComplexPlot3D[fn, {x, x0, x2, (dx)}, {x, x0, x2, (dx)}, (options)]
Plots in the complex plane. The absolute value is represented
by the height and the phase is represented by the color
ComplexMap by Roman Maeder
*CartesianMap[f, {x0, x1, (dx)}, {y0, y1, (dy)}] plots the image
of the cartesian coordinate lines under the function f.
*PolarMap[f, {r0:0, r1, (dr)}, {phi0, phi1, (dphi)}] plots the
image of the polar coordinate lines under the function f.
Transform2DPlot by Xah Lee
http://www.xahlee.org/SpecialPlaneCurves_dir/MmaPackages_dir/Transform2DPlot
_dir/Transform2DPlot.m
This package exports the function Transform2DPlot and
Transform2DGraphics that plot the image of the plane under
arbitrary transformation function f:R^2->R^2 or f:C^1->C^1.
It can be easily adapted to make it plot conformal maps.
It is possibile to write a shell that calls the procedures with a
syntax similar to that of ComplexMap. (years ago I wrote one,
only a few lines long - no big deal since Xah Lee's procedures do
it all. If someone is interested, though, and has already
downloaded the original package by Xah Lee let me know and
I'll send it to them)
ComplexMapPlot by Theodore W. Gray and Jerry Glynn
This one is included in their book "Exploring Mathematics with
Mathematica", Addison-Wesley, 1991. I don't think it is
available on the web. I had found a reference to it in a gallery
of complex functions (I saved it in rtf format without the
pictures!!! How smart : )). But if the original poster has access to
the book he can find out if what it does suits him.
cheers,
Peltio
Invalid address in reply-to. Crafty demunging required to mail me.