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mass production of machines

prequel: how to code individual machines and matching pairs

• are you sure you read the prequel?

• hm.. ye

• anyway, you know how the guy tit for tat is written?
• 1 1 0 1 0
• what about the grim trigger guy?
• 1 1 0 0 0
• ok

rationale

there are two points that explode when they clash into each other:

• each machine has 5 slots in its dna.
• each of these slot can hold only value 0 or 1.

-> there are 2^5 = 32 of them, and they are base-2 numbers:

0 0 0 0 0 -> 0
0 0 0 0 1 -> 1
0 0 0 1 0 -> 2
0 0 0 1 1 -> 3
0 0 1 0 0 -> 4
0 0 1 0 1
...
1 1 1 1 0
1 1 1 1 1 -> 31

this magnificient :D findings rests in the case that machines are deterministic.

mass produce

so let's mass produce them all.

(define (base10->base2 n)
  (~r n #:base 2 #:min-width 5 #:pad-string "0"))

try:

> (base10->base2 31)
"11111"
> (base10->base2 5)
"00101"

so you want to see what is the base10 version of tit-for-tat guy?

> (string->number "11000" 2) ; this is grim-trigger dna
24
> (string->number "11010" 2)
26

anyway, we see that we havent really created automaton, we only convert a base10 number into a string of base2 equivalent. now we have to separate the string (using string->list) into a list of characters then convert the characters into digits:

(define (char->digit c)
  (case c
    [(#\0) 0]
    [(#\1) 1]))

(define (base2->digits a-string)
  (map char->digit (string->list a-string)))

try:

> (base2->digits (base10->base2 24))
'(1 1 0 0 0)

this is clearly the dna of the grim-trigger guy. but this is just a list, it's not yet in automaton structure. we need to do this in order to register this list as an automaton:

> (make-automaton 1 1 0 0 0)
#<automaton>

which is done by using apply:

(define (number->automaton n)
  (apply make-automaton (base2->digits (base10->base2 n))))