User:Salpynx/bf8

Wiki math notation for some functions / formulas to help working with Brainfoctal.

'Length' in base n digits of a number x:

$l(x,n)=\lfloor \log _{n}x\rfloor +1$

Octal digital length:

$l_{8}(x)=\lfloor \log _{8}x\rfloor +1$

Repeat an octal digit x, n times:

$r(x,n)=x{\frac {8^{n}-1}{7}}{\text{ for }}0<x<8$

FizzBuzz (or -4122 -8022)

$\phi =-4122$

$\beta =-8022$

$f(x)=x{\biggl \lceil }{\frac {x}{3}}-\left\lfloor {\frac {x}{3}}\right\rfloor {\biggr \rceil }\times {\biggl \lceil }{\frac {x}{5}}-\left\lfloor {\frac {x}{5}}\right\rfloor {\biggr \rceil }+\beta \left(1+{\biggl \lfloor }{\frac {x}{5}}-\left\lfloor {\frac {x}{5}}\right\rfloor {\biggr \rfloor }\right)+\phi \left(1+{\biggl \lfloor }{\frac {x}{3}}-\left\lfloor {\frac {x}{3}}\right\rfloor {\biggr \rfloor }\right)\times \left(1+9999\left(1+{\biggl \lfloor }{\frac {x}{5}}-\left\lfloor {\frac {x}{5}}\right\rfloor {\biggr \rfloor }\right)\right)$

gives

[1, 2, -4122, 4, -8022, -4122, 7, 8, -4122, -8022, 11, -4122, 13, 14, -41228022, 16, 17, -4122, 19, -8022, -4122, 22, 23, -4122, -8022, 26, -4122, 28, 29, -41228022, ...] ${\text{ for }}x\in \mathbb {N}$

Python equivalent:

from math import floor, ceil
phi = -4122
beta = -8022
fb = lambda x: x * ceil(x/3 - x//3) * ceil(x/5 - x//5) + beta * (1 + floor(x//5 - x/5)) + phi * (1 + floor(x//3 - x/3)) * (1 + (1 + floor(x//5 - x/5)) * 9999)
[fb(i) for i in range(1, 31)]

Truth-machine

${\begin{aligned}G(x,r,m)&=\left\lceil {\frac {\left\vert x\right\vert }{1+x^{2}}}\right\rceil \sum _{i=0}^{m-1}r^{i}\\&=\left\lceil {\frac {\left\vert x\right\vert }{1+x^{2}}}\right\rceil {\frac {r^{m}-1}{r-1}}\\T(x,r)&=G(x,r,\infty )\end{aligned}}$ Where x = input value, r = output radix (suggested = 10), m = number of 'loops' (suggested = ∞ or 100)

Resources

• Esowiki plugin info Special:MathStatus
• wikipedia:Help:Displaying_a_formula