J solution: 197 173 165 161 bytes (so far)
this does not use the method mentioned in the comments to the OP
p=:j./<.-:$g=:1$~(,])n=:<:+:".1!:1]3
d=:j.r=:1
(m=:3 :'if.y<*:n do.if.0=t=:<:t do.d=:d*0j1[t=:<.r=:r+0.5 end.m>:y[g=:y(<+.p=:p+d)}g end.')t=:2
1!:2&2(1 p:g){' *'
