f

#### RE: Re: Re: Suggestion: Visualization of complex functions with Mathematica

```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

From: Peltio [mailto:peltio@twilight.zone]

"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".

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
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

```
 0
djmp (1214)
12/8/2003 7:30:46 AM
comp.soft-sys.math.mathematica 28821 articles. 0 followers.

0 Replies
1148 Views

Similar Articles

[PageSpeed] 23

Similar Artilces:

Re: Re: Re:
>From: David Elliott <elliott@stcnet.com> >To: "Yue Huang" <yue31@hotmail.com> >Subject: Re: Re: Re: >Date: Tue, 9 Dec 2003 23:29:13 -0500 > >On Dec 9, 2003, at 10:41 PM, Yue Huang wrote: > >> >>----- Original Message ----- >>From: "David Elliott" <elliott@stcnet.com> >>Newsgroups: comp.soft-sys.wxwindows >>Sent: Tuesday, December 09, 2003 12:44 AM >>Subject: Re: >> >> >>>You'll notice the code in that wxMac method sets the >>>kFloatingWindowClass Mac...

Re: Re: Re: Mathematica language issues
I think most people this entire discussion does not have any practical importance. Obviously something like this: 2*Unevaluated[1+1] 2 Unevaluated[1+1] is extremly unlikely to have any practical use. After all, we use Unevaluated when we want something to remain unevaluated, whereas here only two things can happen: either one will be left with Unevaluated[something] or the "something" will evaluate. Both of these outcomes are obsiously undesirable. Why should one ever use anything like this in a program? In fact if for some unimaginable reason somone needed this sort of thing and wanted Unevaluated to be removed all he needs to do is to ensure that some transformation that does not change the value of the expression will take place during evaluation. For example, one way to make sure thsi will happen woudl be: a*2*Unevaluated[(1 + 1)/a] 4 Obvioulsy this or a similar method can be used in all cases. There are no imaginable cases where one woudl wihs to be left with Unevaluated, if one wanted that one should use Hold or HoldForm. This also deals with the issue of "unpredictability". But for me that is non issue. I understand that there are some people who love life to be perfectly predictable and go to a great length to ensure that (particularly in the case of election results in certain countries) but there others who find a little unpredictability, experimentation and the sense of discovery t...

RE: RE: Re: Mandelbrot Set & Mathematica
Sorry again, but your previous message said >=, not <=. It's still posted on Google Groups, and I checked to make sure. DrBob www.eclecticdreams.net -----Original Message----- From: AGUIRRE ESTIBALEZ Julian [mailto:mtpagesj@lg.ehu.es] Subject: RE: Re: Mandelbrot Set & Mathematica On Tue, 11 May 2004, DrBob wrote: > Sorry, but that just doesn't work, even after changing =BE to >=. There are > only two colors (even using your rainbow function), and no fractal > "antennae". As noted in a previous message, it should be "<=...

Re: Re: Re: Any Mathematica 6 book yet?
I must agree about the debugger. I was very excited by the release of Workbench 1.0 because of the promise of a good debugger. I even took a course on it. The reality is that Workbench is so hard to use ( I can't bring in my old code and debug changes- it just doesn't work) that I never use it. So I'm back to using Print statements again. I love Mathematica but would love to have an easy to use debugger with break points, etc. Oh well. Cliff Nasser Abbasi <nma@12000.org> wrote: "Murray Eisenberg" wrote in message news:fdf236\$20u\$1@smc.vnet.net... &...

Re: Re: Re: Mathematica language issues #2
So far I could resist the temptation to participate in this discussion. However, in his mail Maxim Rytin presents some examples of which he thinks the result is unpredictable. Maybe there is some interest in how I predict the results of simple commands in which Unevaluated occurs. Of course these examples are of no practical interest. Unevaluated is meant to pass unevaluated arguments to a function body and as such it works perfectly. No one in practice is interested in (1+1)*Unevaluated[2+2]. The basic principle has been clearly explained by Andrzej Kozlowsky. Suppose we have a ...

Re: Re: Mathematica Programmer vs. Programming in Mathematica
> -----Original Message----- > From: Steven T. Hatton [mailto:hattons@globalsymmetry.com] > Sent: 15 December 2005 10:30 > Subject: Re: Mathematica Programmer vs. Programming > in Mathematica > ....... > > I wonder what value there woudl be in trying to explain what makes > > Mathematica "functions" different from functions in > languages such as > > C in a book addressed to readers most of whom have no > knowledge of C > > and are not particualry interested in getting it? > > I suspect you will not find very many people who have never > programmed in Java, C#, or C++ and are likely to use > Mathematica extensively. I'm not really saying the > introduction should use these languages extensively as a > means of contrast. I'm saying that Mathematica should be > introduced very differently from the way these general > purpose languages are introduced. Hang on for a minute - our entire corridor is full of scientists who use Mathematica every day. And only a couple have used even C. Most scientists have grown up with Fortran, right? (at least judging from the way they use Mathematica! ;) So your statement that most Mathematica people start from Java or C is incorrect. > "Everything is an expression" should be explained in terms of > recursive data structures, which they are. Obviously, such a > presentation should i...

Re: Re: Re: Marc Re: Andreessen Re: created Re: the Re: first Re: web Re: browser
no. ...

Re: Re: Complex Analysis using Mathematica
David, Thank you for your response Basically, what I am trying to accomplish is to prove orthogonal conditions of complex eigenfunctions I have a matrix A A=I-Identity matrix And i have the state space eigenvectors phi_real={Re[v]-Im[v],lamda*Re[v]-Im[v]} phi_imag={Re[v]+Im[v],lamda*Re[v]+Im[v]} phi=phi_real+i*phi_imag Where v is the eigenfunction say Sinh[lamda*x] <A*phi,phi>=2*I = --><w1,w2>=Integrate[Transpose[w1]*Conjugate[w2]],{x,0,1}]-->(I don't know whether this is the correct way to go about it) lamda is some imaginary eigenvalue, lamda=a...

Re: Re: EUREKA Re: Types in Mathematica, a practical example
Hi David, Comments are interlaced in the text below, > -----Original Message----- > From: David Bailey [mailto:dave@Remove_Thisdbailey.co.uk] > Subject: Re: EUREKA Re: Types in Mathematica, a > practical example > > Hello, > > If you want to compute with undefined array elements, why not > use subscript elements such as Subscript[a,1,2]. Hmmm, maybe... Let's see ax := {{Subscript[ax, 1, 1], Subscript[ax, 1, 2]}, {Subscript[ax, 2, 1], Subscript[ax, 2, 2]}} is not a good idea, since evaluation of ax gives an infinite loop. (There are o...

Re: Re: Re: Do Mathematica applications EVER get updated?
atul wrote: > I'm not entirely sure what prompts your anxiety, as I have used several > packages over the years, including Time Series, Wavelet Explorer and > Mathematica Link for Excel. While some functions (from both Time > Series and > Mathematica Link) were incorporated into the kernel over time, updates to > ensure compatibility with new versions of Mathematica were timely and > unobtrusive. > This has not been the case for me and I subscribe to "Premier Service". I must always ask (usually more than once) for updates to the "Mec...

Re: Re: Re: mathematica 64-bit for ms windows
On Thu, 14 Feb 2008 01:00:12 -0500 (EST), J=E1nos wrote: > > > On Feb 13, 2008, at 4:04 AM, David Park wrote: > >> But be aware that if you are buying a new computer, from Dell at >> least, and >> you specify a 64 bit microprocessor, you will not necessarily get a >> 64 bit >> operating system, and may not even be able to install a 64-bit >> operating >> system. So if you are looking to use 64-bit Mathematica check out very >> carefully before purchase that you will indeed have a 64-bit operating >> system. >>...

Re: Re: Re: Not Using a Text Editor Interface for Mathematica
For some interesting reading take a look at Chapter 2 in Edward R. Tufte's 'Visual Explanations'. Dr. John Snow found the cause of the 1854 Cholera Epidemic in London by FIRST plotting the case data on a map of London, and THEN doing the analysis. In the case of the Challenger Space Shuttle disaster, although they were aware of the potential problem, the technicians never made the proper graphic that related risk to temperature in past launches and thus failed to present a convincing case for not launching. Maybe graphics doesn't always come before analysis, but ...

Re: Re: Re: Re: Newly Released Mathematica 5.1 Delivers Unmatched Performance for Handling Data
John, I was thinking of angular measurement. The following works... Needs["Miscellaneous`Units`"] Convert[(Pi/4)*Radian, �] 45 � but the following, using an approximate value, does not work because Degree immediately multiplies out undoing the conversion. Convert[1.35 Radian, �] 1.35 The ExtendUnits package at my web site fixes this but at the expense of putting a HoldForm on the degree symbol. Needs["Miscellaneous`V4ExtendUnits`"] 1.35 Radian // ToUnit[�] % // FullForm 77.3493 � Times[77.34930234266115`, HoldForm[Degree]] Since I generally...

Re: Re: Re: Re: No future for DB2
Well, IDS 10 + XPS 9 as open source = Astonishing cool !! J. -----Original Message----- From: "Obnoxio The Clown" <obnoxio@serendipita.com> To: "Jean Sagi" <jeansagi@myrealbox.com> Date: Wed, 27 Jul 2005 22:00:31 +0100 (BST) Subject: Re: Re: Re: No future for DB2 Jean Sagi said: > > Online 5. as open source = Quite cool. But hugely impractical, as it would reveal far too much about IDS to the competition. -- Bye now, Obnoxio "C'est pas parce qu'on n'a rien � dire qu'il faut fermer sa gueule" - Coluche A smile is a gift that is free to the giver and precious to the recipient. But giving someone the finger is free too, and I find it more personal and sincere. Jean Sagi jeansagi@myrealbox.com jeansagi@gmail.com sending to informix-list ...

RE : Re: RE : Re: copulas and SAS
Thanks, I appreciate your comments,I understand that copula is not the appropriate tool to use, what will be the alternative ? Adel David L Cassell <davidlcassell@MSN.COM> a �crit : joewhitehurst@GMAIL.COM replied: > >Adel, > >You may find the following artilce interesting. [article by Thomas Mikosch not copied] This is a really good article, and a really useful point to make. But 55K is a lot of article to copy. Would it have been easier to point to a URL? The people who read SAS-L as a digest and the people who have slow connections are probably not overly thrilled...

Re: Re: Re: Radio Re: Shack Re: TRP-100 Re: Printer Re:
> Also, trim your replies. Leaving a few pages of original text just so > you can add your few lines at the bottom is just insane. > > g. > > -- > Proud owner of F-15C 80-0007 > http://www.f15sim.com - The only one of its kind. > http://www.diy-cockpits.org/coll - Go Collimated or Go Home. > Some people collect things for a hobby. Geeks collect hobbies. > > ScarletDME - The red hot Data Management Environment > A Multi-Value database for the masses, not the classes. > http://scarlet.deltasoft.com - Get it _today_! > --- Synchrone...

Re: Re: Re: Re: Newly Released Mathematica 5.1 Delivers Unmatched Performance for Handling Data #2
Speaking of colors, are any of you aware of a standard color palette or utility that electronically automates conversion of a given color scheme legend to a palette viewable by students who have trichromatic or dichromatic colorblindness? For example, to such people the area below the light blue in this graph http://www.wolfram.com/products/mathematica/usersanduses/experience/images/s urna3dvolume.th.jpg might be viewed as brown instead of a continuous green-yellow-red gradient. While colors are used as teaching tools in math and geography, colorblindness (like nearsightedness) is not a learning disability if a correction for the distortion is made and the colorblind do see some gradient of the light curve shifted more towards red or green. Let me know if you have come across any palette standards (other black-grey-white) that are color blind accessible or colorblind simulation utilities that can be used. Sylvia Hobbs sylvia.hobbs@state.ma.us -----Original Message----- From: John Jowett [mailto:John.Jowett@cern.ch] Subject: Re: Re: Re: Newly Released Mathematica 5.1 Delivers Unmatched Performance for Handling Data David, I still don't have 5.1 but I agree with you that these seem to have be useless and arbitrary changes to Graphics`Colors`. Wolfram should fix it but, if they don't, I suppose it is always possible to keep a copy of the previous Colors.m inside a directory called Graphics in a location that comes earli...

Re: Re: Music to Mathematica
At 03:01 AM 3/30/2004, Matthias.Bode@oppenheim.de wrote: >Hello Steve, hello Marc, > >sorry, I wanted to be concise but was imprecise. > >1. I have music notes (a song) on paper (classical five line system). > >2. I identify (the key) the note(s) and pauses; e.g. "a" (= 440 Hz). (I can >calculate the frequency for each note.) > >3. How to input this information into Mathematica in order to make it *play* >the music? > >4. I do *not* want to write notes in classical notation on paper using >Mathematica. > >5. I used "...

Re: Re: Mathematica slows down
Dr. Bob, Presumably it has to do with whether intermediate results are effectively cached. Note that the order in which calls to Prime are made matters m=10000; r=Range[m]; rr=Reverse[r]; Timing[p=Prime[r];] {0.03 Second,Null} Timing[pr=Prime[rr];] {1.33 Second,Null} p == Reverse[pr] True Consequently, additional inefficiencies in the original algorithm are probably due to the sequencing of the calls to Prime. Here is the original algorithm (except Print) NumP=15000; Timing[For[k=1,k<NumP,k++, Gap[1]=Prime[k+1]-Prime[k]; Gap[2]=Prime[k+2]...

Re: Re: Some bugs in Mathematica
On 12 Aug 2005, at 06:08, Alex wrote: > Kozlowski's posting is wrong from a to z. First, the square root of a > complex number has two branches. One is "positive" and the other is > "negative". So, if we cancel square root in the numerator and > denominator, the worst error we can make is in the sign. There is no > way to justify the fact that Mathematica was unable to do the > simplification. > As for the first sentence above I think I should leave it to others to make the judgement whether it applies to my posting more than to ...

Re: Re: Some bugs in Mathematica
Looking at the sum in more detail: s1[n_] := Sum[x^k*(Gamma[n-k-1/2]*Gamma[k+1/2])/ (Gamma[n-k-1]*Gamma[k+1]),{k,0,n-1}]; Calculating each term separately TableForm[t=Table[(Gamma[n-k-1/2]*Gamma[k+1/2])/(Gamma[n-k-1] *Gamma[k+1]), {n,5},{k,0,n-1}], TableHeadings->{Automatic,Table[i,{i,0,4}]}] Summing each row of the table Tr/@t {0, Pi/2, Pi, (3*Pi)/2, 2*Pi} For example, for n=2, the term for k=0 is ((Gamma[n-k-1/2]*Gamma[k+1/2])/(Gamma[n-k-1]*Gamma[k+1])/. {n->2,k->0}) == Gamma[3/2]*Gamma[1/2]/(Gamma[1]*Gamma[1])== (1/2)*Gamma[...

Re: Re: Types in Mathematica
I like this idea. Does the mathematical/algebraic "programming" style scale up to large problems? Are there examples? Or perhaps it doesn't strictly scale, but is better applied judiciously. It could be used to steer a code at a very high level, or conversely, used in the gaps (the Mathematica-in-the-gaps argument). Conventional programming would make up the difference. If indeed mathematical programming is not the silver-bullet paradigm, where should the conventional (though modern) programming be done? Within or without Mathematica? If within, then we've c...

> I completely agree - can you remember who it was who wrote a > "Mathematica book generator" and posted it here - if you can, > I will add a link to it on my site, because that is all that > we seem to have for the foreseeable future! > > I think WRI's approach to documentation is a real mistake. > Newbies must find it almost impossible to get into the > software. Also, some of the new features of 6.0 - such as all > the new capabilities of Import and Export are almost buried > and unusable because of poor, vague, Microsoft-style document...

Re: Re: Mathematica and Education
What an excellent and encouraging response! Here we have: 1) A skilled teacher who has given much thought on how to use Mathematica in an educational setting and has gained a lot of experience. 2) An institution that has given her serious support. 3) All the students have access to Mathematica all of the time. 4) The students learn Mathematica early in their college career so they will have easy use of it in their more advanced courses. I hope people flock to the University of Vermont to see how it's done. I'm sure there are others also and I hope we hear from some of the...

Web resources about - RE: Re: Re: Suggestion: Visualization of complex functions with Mathematica - comp.soft-sys.math.mathematica

Visualization Software and Tools - VisualizationSoftware.com
Find the most thorough information on visualization software and compare different software programs and methods.

Biological data visualization - Wikipedia, the free encyclopedia
Biology Data Visualization is a branch of bioinformatics concerned with the application of computer graphics , scientific visualization , and ...

Scientific visualization - Wikipedia, the free encyclopedia
Scientific visualization ( also spelled scientific visualisation ) is an interdisciplinary branch of science according to Friendly (2008) "primarily ...

GE Data Visualization
At GE, we believe data visualization is a powerful way to simplify complexity. We are committed to creating visualizations that advance the conversation ...

data visualizations - because information needs to be available
Visualization of basic stats of http://www.pietel.be, combined with autobiographical data mentioned on his blog. Read the rest of this post ...

Facebook Data-Visualization Outfit SumAll Closes \$6M Capital-Financing Round
Data-focused software-as-a-service provider SumAll announced the completion of a \$6 million series-A capital-financing round led by Battery Ventures ...

Facebook Roundup: Privacy Visualization, Topix, Unlikes, Parature and Oil
Visualizing Facebook’s Move Towards Openness — Whatever you think about Facebook’s relentless efforts to make its service more open and central ...