# peteg's blog - hacking - 2008 08 11 FishCycle

## An old friend.

In a previous life I implemented GLog, a declarative graphics engine based on some very old ideas. In this one I've been implementing Peter Henderson's even older Functional Geometry as part of an assignment for JAS. If your browser can render SVG and HCoop's webserver is behaving itself, you should see the dear old "fish cycle" from the paper Logic programming graphics and infinite terms by P. R. Eggert and K. P. Chow.

If you look at the free standing SVG file, you should be able to exercise the scaling feature of the SVG implementation in your browser. The `FLAN` source code is this:

```polyline :: [(Num, Num)] -> [Shape]
polyline pts =
match pts with
[]   -> []
| p:ps ->
let mkP :: (Num, Num) -> [(Num, Num)] -> [Shape]
mkP prev qqs =
match qqs with
[]   -> [] -- Don't close the polygon.
| q:qs -> (Line prev q) : (mkP q qs)
end ;
in mkP p ps
end
;

leftFish :: Picture
leftFish =
Canvas 1 1
((Line (1/8, 3/5) (1, 4/5))
: (polyline [ (1, 1), (1/8, 3/5), (1, 1/8)
, (3/4, 0), (1, 0)]))
;

rightFish :: Picture
rightFish = Flip leftFish
;

fish :: Picture
fish = Beside 1 1 leftFish rightFish
;

sideFish :: Picture
sideFish = Rotate fish
;

matrix :: [[Picture]] -> Picture
matrix = col
;

col :: [[Picture]] -> Picture
col pps =
let mkP :: [[Picture]] -> (Picture, Num)
mkP pps = match pps with
[]   -> (Empty, 0)
| p:ps -> match mkP ps with (pic, n) ->
(Above 1 n (row p) pic, n + 1)
end
end ;
in match mkP pps with (p, n) -> p end
;

row :: [Picture] -> Picture
row pps =
let mkP :: [Picture] -> (Picture, Num)
mkP pps = match pps with
[]   -> (Empty, 0)
| p:ps -> match mkP ps with (pic, n) ->
(Beside 1 n p pic, n + 1)
end
end ;
in match mkP pps with (p, n) -> p end
;

main =
let u :: Picture
u = fish ;
l :: Picture
l = sideFish ;
d :: Picture
d = Rotate l ;
r :: Picture
r = Rotate d ;
in matrix [[d, l,     l],
[d, Empty, u],
[r, r,     u]]
```

There is an implementation available in LISP.