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# [Haskell](https://www.haskell.org) + [hgl](https://gitlab.com/wheatwizard/haskell-golfing-library), 144 bytes

```haskell
k=cy"X.XX"
3#y=[8,9,4,4]!y
2#y=[8,9,8,8]!y
x#1=[4,0]!x
x#3=[0,3]!x
_#_=0
f x y|(n,j)<-fvD 4$x%4#(y%4)=tk y$dr j$tk x<dr n<cy[dr2 k,k,cy"...X",k]
````

[Attempt This Online!](https://ato.pxeger.com/run?1=lZDPaoNAEMbp1acY_wTWslmsbsAEt6cS6C3QiyBiJbrUrJrUanGhD9F7L15Knyl9miq2FwtNc5rfzHwf8zFvHw_xk0jzvDuqWXHYVzU8NnGe8SxNYFOleZOkyvdi897UfO4eXwXbSs0nvq8pji5Z4OIlppiGqlTsn97F7tC3-hULKLZCte3ZYYGFnYEjPWKWwqEF-YJKvDO9OX--AWq0M6ojOaMmqwVII6lgZ_TUej2V3lYGSWWDwAL3EQghvoZFOOb6vLgv4qxkyV4BKCJA6PIaDnegaSZ4w6BnDzggG1YruC1r04TAJmQZntA7Z-rpL_1fhvU00uLUifU01P8c9GzHYuoYH911Y_0C)

I first set up a pretty dense background pattern which doesn't break any rules:

```
XXX.XXX.XXX.XXX.XXX.
X.XXX.XXX.XXX.XXX.XX
...X...X...X...X...X
X.XXX.XXX.XXX.XXX.XX
XXX.XXX.XXX.XXX.XXX.
X.XXX.XXX.XXX.XXX.XX
...X...X...X...X...X
X.XXX.XXX.XXX.XXX.XX
XXX.XXX.XXX.XXX.XXX.
X.XXX.XXX.XXX.XXX.XX
...X...X...X...X...X
X.XXX.XXX.XXX.XXX.XX
XXX.XXX.XXX.XXX.XXX.
X.XXX.XXX.XXX.XXX.XX
...X...X...X...X...X
X.XXX.XXX.XXX.XXX.XX
XXX.XXX.XXX.XXX.XXX.
X.XXX.XXX.XXX.XXX.XX
...X...X...X...X...X
X.XXX.XXX.XXX.XXX.XX
```

All we have to do is make sure the pattern is aligned so there's always a path. I wish I had some clever way of doing this, but I just use a bunch of magic numbers I calculated by trial and error.

Since the pattern repeats with period 4, I just tried every pair of numbers on the range 1-4 and found a shifting that lined up. I encoded these in base 4 and that's what the program uses.

There might be an opportunity to optimize this by finding better numbers.