11 March 2023

This is the source for my Wireworld 1K binary adder. I used Golly to build and save the component in a RLE encoded format, a text-friendly format used directly in the code. See references at the bottom for the format. I commented the source after the Jam. I would not have satisfied the 1K limitation otherwise :)

*Image of the binary adder as implemented in Golly*

## Commented Source

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pico-8 cartridge // http://www.pico-8.com
version 37
__lua__
w,h=100,15 -- constant: size of the adder.
ini=split"32,26,20,14,8,2" -- a lookup table of the x-positions for each of the input bits.
oui=split"91,85,79,73,67,61" -- a mystery line that never got used, left for your amusement.
function bits(n,y,i) -- function: set bits ON for input Y given number N.
-- this travels through each bit in a number and sets
-- the CA cell to an electron if the bit is on.
i=1 -- * start at first bit.
while n>0 do -- * while number is positive.
r=n%2 -- * get modulo 2 of number (even numbers yield 0).
n=(n-r)/2 -- * reduce number by result of above, then halve it.
if r==1 then -- * if number is odd.
x=ini[i] -- * lookup the x position for this bit.
ww[y][x]=12 -- * set electron head.
ww[y][x-1]=7 -- * set electron tail.
end
i+=1 -- * move to next bit.
end
end
function _init() -- program entry.
poke(0x5f5c,30) -- set custom keypress delay to 30 ticks,
poke(0x5f5d,30) -- repeat for key-repeat.
ww={} -- storage for the wireworld cells.
tf={a=12,b=7,c=9} -- there are three states in wireworld:
-- * copper wire (orange:9)
-- * electron tail (white:7)
-- * electron head (blue:12)
-- a fourth color (green:3) is our insulator.
-- next up we have our binary adder in RLE form.
-- the split function returns a table of values
-- split at commas (these demarcate the rows).
r=split"2c4.2c4.2c4.2c4.2c4.2c15.6c,46.c6.c5.2c4.2c4.2c4.2c4.2c4.2c4.2c,37c5.4c2.2c2.4c,37.c3.c5.c2.b.c2.42c,4c2.c.c4.2c3.c.c3.2c5.c4.4c.c3.c.2ca2.4c,.c.c2.c.2c3.2c3.3c4.c5.c4.c2.2c.5c6.c3.c.c.c2.4c3.c.c4.2c3.c.c3.2c5.c,2c.2c.c.2c3.2c5.c4.2c4.c4.4c.c3.c.c4.c4.5c3.c.c3.c.2c3.2c3.3c4.c5.c,37.c3.c5.c3.c5.2c2.c2.2c.2c2.c.2c3.2c5.c4.2c4.c,38c2.3c3.3c.c,38.c2.c5.c2.c,2c4.2c4.2c4.2c4.2c4.2c6.c.c.c3.c.2c,38.c.c.c3.c.c,39.c2.c2.3c,42.c3.c,43.3c"
for y=1,#r do -- this loop decodes the RLE:
ww[y]={} -- add a new row to ww.
d=r[y] -- store this row string in d.
m=""
for x=1,#d do -- process each character in d.
v=d[x]
if tonum(v) then -- concat numbers together.
m..=v
else
p=tonum(m) or 1 -- parse numbers, defaults to 1.
for n=1,p do -- lookup value v in tf (defaults to insulator 3)
add(ww[y],tf[v] or 3) -- then add it p-times to the world.
end
m=""
end
end
end
tm=1 -- set a timer.
fx=1 -- set state (1: wait for button press)
st="" -- clear status text.
end
function _update() -- update loop.
tm-=1/2 -- reduce timer.
if fx==0 and tm<0 then -- test if in running state.
print"\ac1g" -- bip-bip-bip.
tm=btn()>0 and 0 or 1 -- speed up simulation by holding button.
ti+=1 -- step CA generation.
cp={} -- storage for next generation.
for y=1,h do -- evolve each cell in wire world:
cp[y]={} -- * new row.
for x=1,w do -- * next column.
cp[y][x]=tnb(x,y,ww[y][x]) -- * transform and store new cell value via tnb call.
end -- I don't recall what tnb means.
end -- let's go with tasty new bananas. that works.
ww=cp -- persist the new generation.
if ti==66 then -- the calculation is complete, show the answer.
fx=1 -- 66 is the number of generations to solve the problem.
ans="="..a+b
end
elseif btnp()>0 then -- button pressed.
if fx==1 then -- in waiting state.
ans=nil -- reset calculation state.
ti=0 -- ...
fx=2 -- ...
a=flr(rnd(63)) -- pick random number "a".
b=nil -- empty "b".
bits(a,3) -- set a-bits.
st="rolling dice"
elseif fx==2 then
fx=3 -- ...
b=flr(rnd(63)) -- pick random number "b".
bits(b,9) -- set b-bits.
elseif fx==3 then -- end of calculation state.
st="" -- ...
fx=0 -- ...
end
end
end
function _draw() -- render loop.
cls(3) -- ...
print("\^pwireworld",1,1,10)
print("binary adder",74,5,11)
print("\^ipico-1k jam 2022",30,14,15)
print(st,4,122,7)
for y=1,h do -- plot the current state of wire world cells.
for x=1,w do
pset(x+13,y+60,ww[y][x] or 3)
end
end
print(a or "",5,59,14) -- not much else to see here,
if(a)print("+",2,64,14) -- unless you love reading
print(b or "",5,69,14) -- "print" and "or".
print(ans or "",112,61,11)
if fx==0 and flr(time())%2==0 then print("working",4,122,10)end
end
function tnb(x,y,o,c) -- function: evolves a wireworld cell.
-- this is the crux of wireworld, the
-- brevity of this function is exemplary
-- to the simplicity of this CA.
-- the rest of the code is only
-- data-and-state management.
-- the arguments are:
-- * x,y: cell coordinate.
-- * o: current value.
-- * c: not passe1 (variable optimization).
if o==12 then return 7 -- head turns to tail.
elseif o==7 then return 9 -- tail turns to copper.
elseif o~=9 then return o end -- non-copper (insulator) stays as-is.
c=0 -- this code is only reached for copper (9):
for a=-1,1 do -- it counts the number of
for b=-1,1 do -- electron heads in the moore-neighborhood region
if ww[y+a] and ww[y+a][x+b]==12 then
c+=1
end
end
end
return c>0 and c<3 and 12 or o -- turn into electron head if
end -- the cell has 1 or 2 neighbors,
-- otherwise it stays as-is.

Here is the Golly version saved as RLE:

```
#CXRLE Pos=-50,-7
x = 97, y = 15, rule = WireWorld:P100,15
2C4.2C4.2C4.2C4.2C4.2C15.6C$46.C6.C5.2C4.2C4.2C4.2C4.2C4.2C4.2C$37C5.
4C2.2C2.4C$37.C3.C5.C2.B.C2.42C$4C2.C.C4.2C3.C.C3.2C5.C4.4C.C3.C.2CA
2.4C$.C.C2.C.2C3.2C3.3C4.C5.C4.C2.2C.5C6.C3.C.C.C2.4C3.C.C4.2C3.C.C3.
2C5.C$2C.2C.C.2C3.2C5.C4.2C4.C4.4C.C3.C.C4.C4.5C3.C.C3.C.2C3.2C3.3C4.
C5.C$37.C3.C5.C3.C5.2C2.C2.2C.2C2.C.2C3.2C5.C4.2C4.C$38C2.3C3.3C.C$
38.C2.C5.C2.C$2C4.2C4.2C4.2C4.2C4.2C6.C.C.C3.C.2C$38.C.C.C3.C.C$39.C
2.C2.3C$42.C3.C$43.3C!
```

# References

# Journal

Date | Title |
---|---|

11 Mar 2023 | source code |