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2 Simple Maps     continued...

In Figure 4, we present a picture of the Hénon attractor for a fairly large number of points (). If one could increase the number of points by one or two orders of magnitude, the self-similarity inherent in the attractor would manifest itself, as we show in Figure 5.

Figure 4 x--y plot of the Hénon attractor. The diagram was created by first executing a fortran program with initial values and ; 10,000 iterations were performed and the calculated points plotted with xmgr.

Figure 4: Plot of the Henon attractor

Click here to calculate and plot the Henon map.

Figure 5 Pictures illustrating self similarity for the Hénon attractor. The diagram was created by first executing a fortran program with initial values and ; 50,000 iterations were performed and the calculated points plotted with xmgr. The xmgr ``magnifying glass'' was used successively to zoom in on the regions indicated by the rectangles.

Figure 5: Pictures illustrating self similarity for the Henon Attractor.