The idea of delay coordinates is simple. It is important to choose a good value for T, the delay. If the delay is too long, then the coordinates are essentially independent and no information can be gained from the plot. This can be seen in the next section . For more information on information theory and this method, you should read the article.
Information theory is interesting stuff.
I did this one first as it's the test case that Fraser and Swinney use. Fortunately my graph resembles their graph, proving that I didn't make any mistakes writing the software. In the next section you can see what the attractor looks like for these two choices. This graph looks much different, which is not suprising. Recall that the for the periodic time series, the period was 6.9 seconds.