IBM Ponder This #151 · November 2010

November's challenge is dedicated to IBM Fellow Benoît Mandelbrot, who died on October 14, 2010, at the age of 85.

Let's define a function f on five variables (i, j, k, l, and m) as follows:

If (i-m)*(j-m) is zero then
    f(i,j,k,l,m) ← ((abs(j-(1-k+l)*m)-m+1)* (abs(i-(k+l)*m)-m+1))
else
    f(i,j,k,l,m) ← f(i mod m,
                           j mod m,
                          int(((i^j)&((m*l)^i))/m)^l^k^int(i/m),
                          int(((i^j)&((m*k)^i))/m)^l,
                          m/2)

Where
x^y      means bitwise xor (exclusive or)
x&y     means bitwise and (conjunction)
abs    is the absolute value
mod   is the modulo function
int       means truncating downwards to an integer

What should be the input to the function f, and how do you need to interpret its output to associate it with Professor Mandelbrot?

Update: November 5th: We are *not* looking for his age.

Update: December 1st: m is a power of 2.

Solution

Best opened after a real attempt

To be added.