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MathGroup Archive 2003

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Re: New Plot output in version 5

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44274] Re: New Plot output in version 5
  • From: Bill Rowe <readnewscix at mail.earthlink.net>
  • Date: Tue, 4 Nov 2003 03:23:44 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On 10/31/03 at 3:01 AM, mjankowski at usm.maine.edu (Mariusz Jankowski) wrote:

> I just noticed that Plot no longer obeys the domain limits given by its second 
> argument. Try the following to reproduce my result:
 
> Plot[UnitStep[x], {x,-1,5}]

> This cannot possibly be a feature change, can it? 

No, this feature has been in Mathematica before version 3. (I can't recall whether it was in earlier versions but I suspect that it was.)

> I know I can force the desired behavior by using PlotRange, but why should I need to repeat myself? 

The algorithm in Mathematica is designed to scale the plot to show the most "interesting" features of the curve plotted. For the most part, it works quite well. In fact, surprisingly well if you think about the difficulty of defining "interesting" in an unambiguous way. Since there really is no apriori way for Mathematica to know what aspect of a plot will be most interesting to you, any choice will result in a plot other than what you want at some point.

Consider the problem of plotting data from some set of measurements. If there is one extreme point, an outlier, a plot showing it and all the other points likely obscures the trend shown by the other points. OTOH, the one extreme point could be the most significant data point rather than of no interest. How would you choose default plot options in this case?
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