Re: Plotting a function -
- To: mathgroup at smc.vnet.net
- Subject: [mg71691] Re: Plotting a function -
- From: "Ray Koopman" <koopman at sfu.ca>
- Date: Sun, 26 Nov 2006 05:49:31 -0500 (EST)
- References: <ek990u$k88$1@smc.vnet.net>
Craig Reed wrote:
> Hi -
>
> I'm trying to get Mathematica 5.2 to graph a function which is the ratio of
> integers which have a '3' in them. Done in Exce3l, the graph of the first
> 32,000 data points has a fractal look to it, especially when done with a
> log scale.
>
> What I've tried is the following
>
>
> f[x_] := Boole[DigitCount[x, 10, 3]]
> g[x_] := Sum[f, {i, x}]/x
> Plot[g, {x, 1, 100}]
>
>
> I get 3 errors of "g is not a michine-size real number at" followed by 3
> real numbers:
> 1.000004125
> 5.016125.....
> 9.39607.....
>
> What am I doing wrong? or perhaps what I should ask is, "Is there a better
> way?"
If f[x] is supposed to give a numeric indicator of whether or not the
decimal representation of an integer 'x' has a '3' in it, then try
f[x_Integer] := Boole@MemberQ[IntegerDigits@x,3]
If the numerator of g[x] is supposed to be the number of values
in the range 1,...,x for which f gives '1', then you could say
g[x_Integer] := Sum[f[i], {i, x}]/x
There are other ways to get g, some of which may be much faster
but less obvious.
To get the plot you could do
ListPlot[Table[g[x],{x,100}]]
Again, there are other ways to do it, but this is clearest.