Belle Delphine I'm Back

submitted by skeeter from youtube.com

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[–]eh-non-plus 0 insightful - 1 fun0 insightful - 0 fun1 insightful - 1 fun -  (3 children)

solve the collatz problem or the rule 30 prize with me instead

[–][deleted] 1 insightful - 1 fun1 insightful - 0 fun2 insightful - 1 fun -  (2 children)

U think i share? Rly

[–]eh-non-plus 0 insightful - 1 fun0 insightful - 0 fun1 insightful - 1 fun -  (1 child)

Alright, I'll go first. Here's a recursive description of f'(n) = 3n+1 where n is in binary:

f 1      →  11                                                                                                                
f 1ʸ     →  101ʸ⁻²01                                                                                                          
f 10ᵛ n  →  110ᵛ⁻¹        (f n)                                                                                              
f 1ʸ0 n  →  101ʸ⁻²0       (f' n)                                                                                             
f 1ʸ0ʷ n →  101ʸ⁻²010ʷ⁻²   (f n)                                                                                              

f' 1ᵛ     →  01ᵛ⁻¹01                                                                                                          
f' 1ᵛ0 n  →  01ᵛ⁻¹0       (f' n)                                                                                             
f' 1ᵛ0ʸ n →  01ᵛ⁻¹010ʸ⁻²   (f n) 

y w > 1                                                                                                                      
v   > 0

[–]eh-non-plus 0 insightful - 1 fun0 insightful - 0 fun1 insightful - 1 fun -  (0 children)

Notice how divide by two only removes redundant information (namely all leading zeros on the left of the binary string - little endian) therefore f' (corecursive with f(n) = 3n) is the only entropy-adding element of the collatz problem in binary