genius-common 1.0.23-3 / usr / share / genius / examples / cantor.gel

# Category: Analysis
# Name: Cantor's devil staircase function (approximation)

function Ternary(x,n) = (
    # only if x in [0,1)
    out = null;
    for k = 1 to n do (
        x = x*3;
        fx = floor (x);
        x = FractionalPart (x);      
        out = [out, fx]
    )
);

# Cantor function, only really for x in [0,1]
function Cantor(x) = (
    if x >= 1 then return 1;
    if x <= 0 then return 0;
    # Number of steps, the higher the number the more precise the graph
    n = 20;
    t = Ternary(x,n);
    N = n;
    for k = 1 to n do (
        if t@(k) == 1 then
            (N = k; break)
    );

    1/(2^N) + sum k = 1 to (N-1) do (t@(k)/(2^(k+1)))
);

PlotWindowPresent(); # Make sure the window is raised
LinePlot(Cantor,[0,1]);