Iterate a user defined function to load Table or ParametricPlot function

Questions
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1

I would like to plot series of points on a graph starting at a given point and continuing to the point of greatest magnitude. This could be accomplished by either creating a Table[] of points and then plotting the points, or embedding ParametricPlot[] in the Show[] function. However using either Table[]or ParametricPlot [] functions would require iterating a user defined gradient function and then using the output of the previous iteration as the input to the subsequent iterations and I am not sure how to do that in Mathematica and would appreciate guidance in performing the iterations (see attached notebook).

Additional if my whole approach is incorrect, I would be open to any and all suggestions because I am always interested it trying a better method to visualize my calculations.

Thank you so much for your assistance.

ParametricPlotQuestion.nb (709 KB)

2

Hi Mitchell,

iterating a user defined gradient function and then using the output
of the previous iteration as the input to the subsequent iterations

Nest and related functions can do this e.g.

NestList[Normalize@df[Sequence @@ #] &, {3, 4}, 3]
(* {{3, 4}, {7/25, -(24/25)}, {527/625, 336/625}, {-(164833/390625), -(354144/390625)}} *)

In the attached notebook P1, P2, P3, P4 ignore the sign of the previous term. If that is what you want, just add an Abs.

3

Hi Rohit;

I included your NestList[] iterator into my Graphics[] function replacing the points (P1, P2, P3, and P4) which I had created manually and your code worked great in duplicating what I had created manually.

However, the location of plotted points is still somewhat concerning. What I was expecting was a sequence of points that follow the VectorPlot[] function in somewhat a uniform spacing and approach the greatest temperature, which the points do not.

I am in the process of rewriting my discussion and plan to resubmit it tomorrow for additional comments. Hopefully, I will do a better job explaining my concerns.

Thanks,

Mitch Sandlin