IBM Research | Ponder This | November 2010 challenges

Ponder This

November 2010

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Ponder This Challenge:

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.

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com

Challenge: 11/02/2010 @ 10:30 AM EST
Solution:
List Updated: 11/02/2010 @ 10:30 AM EST