# Can I represent a computer program on a Hilbert Curve?

I overheard in discussion tonight:

You know - you can represent a computer program as points on a Hilbert Curve.

Is there a reference that explains this concept? I can't seem to Google for it.

• I'm not sure about the Hilbert Curve reference, but since the Hilbert Curve is continuous and space-filling it's equivalent to representing a program as a point in the unit square. You can just as easily represent a computer program as a real number between (0,1) by transforming the program into binary, concatenating the digits, and prepending a $0.$ – Foo Barrigno Aug 28 '14 at 13:35
• That would be a rational number, to be more precise. Of course, why not just use a natural number? (I'd say the question is too vague.) – Radu GRIGore Aug 28 '14 at 19:30