# Animation of graphing a function

Do anybody have a program which shows a computer graphing a function pointwise in stages? For example:

At stage 1, it graphs all the integer x values

Stage 2, all the multiples of 1/2

Stage 3, all the multiples of 1/4

and so on until we have a full picture of a continuous function.

A single continuous animation of random points being plotted until it fills in a continuous graph would be just as good.

Comment if you are interested in this. I might try my hand at making one if nobody has already.

This is pretty straightforward in Mathematica:

f[x_] := x^2;
xrangeleft = -2;
xrangeright = 2;
yrange = {0, 4};
xrange = {xrangeleft,xrangeright};
frames = Table[ListPlot[Table[{x, f[x]}, {x, xrangeleft, xrangeright, 1/2^i}],
PlotRange -> {xrange, yrange}], {i, 0, 10, 1}]
Export["FunctionPlot.gif", frames]


(You might need to use Directory[] to find out where it exported your file.)

This creates the following: Here is the code in Matlab for the sine function:

for k = 0:6
n=2^k          % stage number, k=0: integer values, k=1: stage 2, ...
x=0:1/n:3*pi;
y = sin(x);    % sine function
pause(1);      % pause duration
plot(x,y,'b.')
axis ([0 3*pi -1.5 1.5])
grid on
end


If I may suggest a tiny variation on Aeryk's nice code, to slow it down, and join the dots: f[x_] := x^3;
xrangeleft = -2;
xrangeright = 2;
yrange = {-8, 8};
xrange = {xrangeleft, xrangeright};
frames = Table[
ListPlot[Table[{x, f[x]}, {x, xrangeleft, xrangeright, 1/2^i}]
, Joined -> True
, Mesh -> Full
, PlotRange -> {xrange, yrange}]
, {i, 0, 3, 1}];
Export["FunctionPlot.gif", frames, "DisplayDurations" -> 3.0]