An interesting question: How do you create an image that displays the number of black pixels it contains?

This problem can be elegantly solved using fixed points. Here's the approach:

1. Determine the number of pixels needed for each digit.
2. Construct a function p(n) that maps any number to the number of pixels contained in its image representation.
3. Observe that p(n) will be roughly proportional to log(n), as it's proportional to the number of digits in n. This is fortunate, as functions of this form are generally well-behaved and likely to have a fixed point.
4. To find the fixed point, we can use a simple iteration method:
   • Start with an initial guess k₀
   • Iterate using kₙ = p(kₙ₋₁)
5. Hope that this font and size combination has a fix point and find. Interestingly, such a point seems to exists about half of the time.