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MathGroup Archive 2006

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Re: recursive blues :(

  • To: mathgroup at smc.vnet.net
  • Subject: [mg70315] Re: recursive blues :(
  • From: dimmechan at yahoo.com
  • Date: Thu, 12 Oct 2006 05:38:13 -0400 (EDT)
  • References: <egi1qo$jaa$1@smc.vnet.net>

Your syntax is completely wrong.
Try

Clear[f]
f[x_] := f[x + 2] /; x < -2^(-1)
f[x_] := f[x - 2] /; x > 3/2
f[x_] := 2 /; -2^(-1) < x < 1/2
f[x_] := 1 /; 1/2 < x < 3/2

Then execute the following command to get a plot

Plot[f[x], {x, -3 3}, Frame -> {True, True, False, False}, Axes ->
False,
ImageSize -> 400]
(*plot to be displayed*)

If you want not to displayed the undesirable vertical lines connecting
the discontinuities you can use the following one-liner which modifies
slightly the Plot function.
(see also
http://groups.google.gr/group/comp.soft-sys.math.mathematica/browse_thread/thread/ece0e44f7b2f8600/df67129bb8472a9f?lnk=gst&q=plotDisc&rnum=1#df67129bb8472a9f
)

plotDisc[g_, x_, a_, b_, c___, {opts___}] := Show[(Plot[g, {x, #1[[1]],
#1[[2]]},
opts, DisplayFunction -> Identity] & ) /@ Partition[{a, c, b}, 2, 1],
DisplayFunction -> $DisplayFunction]

Then

plotDisc[f[x], x, -3, 3, -2.5, -1.5, -0.5, 0.5, 1.5, 2.5, {Frame ->
True, Axes -> False, PlotStyle -> Red}]
(*plot to be displayed*)

Let see one other way of defining your f function.

If you have Mathematica version 5.1 and newer you can use the following
definition

Clear[f]

f[x_] := Piecewise[{{f[x + 2], x < -2^(-1)}, {f[x - 2], x > 3/2}, {2,
-2^(-1) < x < 1/2},
{1, 1/2 < x < 3/2}}]

Plot[f[x], {x, -3, 3}]
(*plot to be displayed*)

(my plotDisc cannot be applied here...)

Regards
Dimitris


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