Re: Plotting a function -

*To*: mathgroup at smc.vnet.net*Subject*: [mg71650] Re: Plotting a function -*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Sun, 26 Nov 2006 03:48:32 -0500 (EST)*Organization*: The Open University, Milton Keynes, UK*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?" > Craig, The corrected version of your code I gave you in my previous email is very slow indeed. You will find below a functional code that is much faster. In[1]:= f[x_] := Boole[DigitCount[x, 10, 3] > 0] g[x_] := Sum[f[i], {i, x}]/x Plot[Evaluate[g[x]], {x, 1, 100}]; In[4]:= Timing[Plot[Evaluate[g[x]], {x, 1, 100}]; ] Out[4]= {0.609 Second,Null} In[5]:= Timing[Plot[Evaluate[g[x]], {x, 1, 1000}]; ] Out[5]= {23.282 Second,Null} In[23]:= Timing[rng = Range[1, 100]; ListPlot[Rest[FoldList[Plus, 0, (Boole[DigitCount[#1, 10, 3] > 0] & ) /@ rng]]/ rng]; ] Out[23]= {0.015 Second,Null} In[24]:= Timing[rng = Range[1, 1000]; ListPlot[Rest[FoldList[Plus, 0, (Boole[DigitCount[#1, 10, 3] > 0] & ) /@ rng]]/ rng]; ] Out[24]= {0.078 Second,Null} In[25]:= Timing[rng = Range[1, 10000]; ListPlot[Rest[FoldList[Plus, 0, (Boole[DigitCount[#1, 10, 3] > 0] & ) /@ rng]]/ rng]; ] Out[25]= {1.141 Second,Null} In[26]:= Timing[rng = Range[1, 100000]; ListPlot[Rest[FoldList[Plus, 0, (Boole[DigitCount[#1, 10, 3] > 0] & ) /@ rng]]/ rng]; ] Out[26]= {7.859 Second,Null} Regards, Jean-Marc