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Julia Set of p(z) = z^2 - 0.52 + i 0.57  Complex Plot Home 

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Please email P. Bourdon with any questions or comments you might have about Cplot or this Web site.

Development of Complex Plot was based upon work supported by the National Science Foundation under Grant No. 9706614 (as well as Grant No. 9401206 and No. 9023427).

Any opinions, findings and conclusions or recomendations expressed at the Complex Plot site are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).

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What is Complex Plot?

Complex Plot is a mathematical application used to plot images of complex-valued functions of a complex variable. The Complex Plot project history is a long one; the project has gone from simple Pascal routines to a full-featured application. The software was developed by a number of students of Prof. Paul Bourdon at Washington and Lee University for use in his research on composition operators. The program (also known as Cplot) was written in C++ using the V GUI library, a cross-platform windowing library; click here for more information on Cplot's development and operation. In short, Cplot is a menu-driven application that plots complex-valued functions on a 2-D canvas.

Why Complex Plot?

Complex Plot was developed because the two major mathematical software packages, Waterloo's Maple V and Wolfram's Mathematica do not include routines to plot images of certain intertwining maps such as Koenigs eigenfunctions; moreover, when Maple and Mathematica are programmed to compute intertwining-map images, execution of the resulting code is painfully slow. Enter Cplot, which plots function and intertwining map images currently at rates up to 500% faster than Maple.

Example Plots

All of the example images were created using Cplot under varying plotting parameters.

Example 1:  z/(2-z^5) Example 2:  z^3/(1-z)
Image of unit disc under f(z) = z/(2 - z5) Image of unit disc under f(z) = z3/(1- z)

More examples (Warning: example page may take several minutes to download over modem connections)