A tetraview is a visualization technique for bivariate complex functions. In the simplest case, the graph of a complex-valued function 
can be considered as a hypersurface in 
with four real coordinates ![(R[z],I[z],R[w(z)],I[w(z)])](/images/equations/Tetraview/Inline3.svg)
. Carrying out a rotation in four
dimensions and projecting the first three coordinates into (ordinary) 
then allows the changes from ![(R[z],I[z],R[w(z)])](/images/equations/Tetraview/Inline5.svg)
to ![(R[z],I[z],I[w(z)])](/images/equations/Tetraview/Inline6.svg)
to ![(R[w(z)],I[w(z)],R[z])](/images/equations/Tetraview/Inline7.svg)
to ![(R[w(z)],I[w(z)],I[z])](/images/equations/Tetraview/Inline8.svg)
to be visualized continuously.
Tetraview
See also
Pólya PlotThis entry contributed by Michael Trott
Explore with Wolfram|Alpha
References
Banchoff, T. "Surfaces Beyond the Third Dimension." http://www.math.brown.edu/~banchoff/art/PAC-9603/tour/wall-1a.html.Banchoff, T. "The Mathematics of the Tetraview." http://www.math.brown.edu/~banchoff/art/PAC-9603/tour/tetra-Z2/tetra-math.html.Banchoff, T. "A Virtual Reconstruction of a Virtual Exhibit." In Multimedia Tools for Communicating Mathematics. Papers from the International Workshop Held at the University of Lisbon, Lisbon, November 2000 (Ed. J. Borwein, M. H. Morales, K. Polthier, and J. F. Rodrigues). Berlin: Springer-Verlag, Berlin, pp. 29-38, 2002.Banchoff, T. F. "Computer Graphics in Mathematical Research, from ICM 1978 to ICM 2002: A Personal Reflection." In Proceedings of the 1st International Conference held in Beijing, August 17-19, 2002 (Ed. A. M. Cohen, X.-S. Gao, and N. Takayama). Singapore: World Scientific, pp. 180-189, 2002.Banchoff, T. and Cervone, D. P. "Understanding Complex Function Graphs." Commun. Visual Math. 1, July 1998. http://www.math.union.edu/~dpvc/CVM-07-98/1998/01/ucfg/.Referenced on Wolfram|Alpha
TetraviewCite this as:
Trott, Michael. "Tetraview." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Tetraview.html