Submitted by MGA on

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SmallBASIC implementations:

The basic idea behind coding is systematic replacement of one symbol or set with another.

Here is example of replacing a 0 with 010 and a 1 with 110, this leads to an expanding set of symbols.

For "an a" type coding* a very interesting thing happens in the expansions.

Try different replacements for 0 and 1, say 0 = "01" and 1 = "10" or "11"

Try for different substitutions of different amounts of 0

0 = 1011 , 1 = 0100...

See a pattern?

* note: from "Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning" by Clifford Pickover, Oxford 2001. Chapter 69 p 167 "An A?"

Here is example of replacing a 0 with 010 and a 1 with 110, this leads to an expanding set of symbols.

For "an a" type coding* a very interesting thing happens in the expansions.

t$ = "0"

for r = 1 to 5

s$ = t$ : t$ = ""

for i = 1 to len(s$)

c$ = mid(s$, i, 1)

if c$ = "0" then t$ = t$ + "010" else t$ = t$ + "110"

next

print t$ : ?

next

Try different replacements for 0 and 1, say 0 = "01" and 1 = "10" or "11"

Try for different substitutions of different amounts of 0

*'s and 1's.*0 = 1011 , 1 = 0100...

See a pattern?

* note: from "Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning" by Clifford Pickover, Oxford 2001. Chapter 69 p 167 "An A?"