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MathGroup Archive 2006

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RE: Plot Sequencies of Complex Functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg67048] RE: [mg67034] Plot Sequencies of Complex Functions
  • From: "David Park" <djmp at earthlink.net>
  • Date: Thu, 8 Jun 2006 04:53:12 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Eleanna,

Here is a table of powers for a sample complex point z. (I suppressed the
output for the posting.)

complexpoints = Table[(0.6 + 0.5I)^n, {n, 1, 20}];

The following converts the complex numbers to a Point with x and y
coordinates.

coordpoints = Point[{Re[#], Im[#]}] & /@ complexpoints;

The following then plots the series of points.

Show[
    Graphics[
      {AbsolutePointSize[5], coordpoints}],
    AspectRatio -> Automatic,
    Frame -> True,
    Axes -> True, AxesStyle -> Gray,
    ImageSize -> 450];

With the Cardano3 package you can use graphical primitives that directly use
complex numbers. So in the following we Map ComplexPoint directly onto the
complex numbers. There are also routines such as ComplexLine, ComplexCircle,
ComplexText, ComplexArrow and ComplexCurve for plotting complex expressions
as curves.

Needs["Cardano3`ComplexGraphics`"]

Draw2D[
    {AbsolutePointSize[5],
      ComplexPoint /@ Table[(0.6 + 0.5I)^n, {n, 1, 20}]},
    AspectRatio -> Automatic,
    Frame -> True,
    Axes -> True, AxesStyle -> Gray,
    ImageSize -> 450];

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/


From: Eleanna Tsoumani [mailto:eleanna_tsoumani at yahoo.gr]
To: mathgroup at smc.vnet.net


Hi all,

  I am trying to graph sequencies of complex numbers (for instance, z^n),
but I cannot come up with a working idea.
  Does anyone have any suggestions?

  Many Thanks to all readers,
  Eleanna





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