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#Scala, 211 Bytes

val b=Array.fill(150)('.')
def s(y:Int,x:Int):Int={val r=Random.nextInt(6)
val z=y+(if(y>3)-r%2
else if(y<1)r%2
else r/2-1)
b(z*30+x)='$'
z}
(3/:(0 to 28))(s(_,_))
b.mkString("").sliding(30,30).foreach(println)

sample:

...................$$$...$.$$.
.$$$..............$...$.$.$...
$...$$$..$...$$.$$.....$......
.......$$.$.$..$..............
...........$..................

degolfed:

val buf = List.fill(150)('.').toBuffer
def setRowCol (y:Int, x:Int): Int = {
  val r = Random.nextInt(6)
  val z = y + (
    if (y>3) 
        -(r%2)
    else if (y<1) 
        (r%2)
    else 
        r/2-1
  )
  buf (z * 30 + x) = '$'
  z
}
(3 /: (0 to 28)(setRowCol (_, _))
println 
buf.mkString ("").sliding(30,30).foreach(println)

My unique invention - well, I haven't read the other solutions so far, is, to generate a Random (6) which is implicitly two Randoms, (2*3). If away from the border, I use the values of r/2 (0,1,2) and → (-1,0,1) tell me, to go up or down. If at the border, I can avoid the character costly call of another random, and just take the modulo(2), to decide, should I stay or should I go.

Let's see the other solutions. :)

#Scala, 207 Bytes

val b=Array.fill(150)('.')
def s(y:Int,x:Int)={val r=Random.nextInt(6)
val z=y+(if(y>3)-r%2
else if(y<1)r%2
else r/2-1)
b(z*30+x)='$'
z}
(3/:(0 to 28))(s(_,_))
b.mkString("").sliding(30,30).foreach(println)

sample:

...................$$$...$.$$.
.$$$..............$...$.$.$...
$...$$$..$...$$.$$.....$......
.......$$.$.$..$..............
...........$..................

degolfed:

val buf = List.fill(150)('.').toBuffer
def setRowCol (y:Int, x:Int): Int = {
  val r = Random.nextInt(6)
  val z = y + (
    if (y>3) 
        -(r%2)
    else if (y<1) 
        (r%2)
    else 
        r/2-1
  )
  buf (z * 30 + x) = '$'
  z
}
(3 /: (0 to 28)(setRowCol (_, _))
println 
buf.mkString ("").sliding(30,30).foreach(println)

My unique invention - well, I haven't read the other solutions so far, is, to generate a Random (6) which is implicitly two Randoms, (2*3). If away from the border, I use the values of r/2 (0,1,2) and → (-1,0,1) tell me, to go up or down. If at the border, I can avoid the character costly call of another random, and just take the modulo(2), to decide, should I stay or should I go.

Let's see the other solutions. :)

#Scala, 219 Bytes

val b=List.fill(150)('.').toBuffer
def s(y:Int,x:Int):Int={val r=Random.nextInt(6)
val z=y+(if(y>3)-r%2
else if(y<1)r%2
else r/2-1)
b(z*30+x)='$'
z}
(3/:(0 to 28))(s(_,_))
b.mkString("").sliding(30,30).foreach(println)

sample:

...................$$$...$.$$.
.$$$..............$...$.$.$...
$...$$$..$...$$.$$.....$......
.......$$.$.$..$..............
...........$..................

degolfed:

val buf = List.fill(150)('.').toBuffer
def setRowCol (y:Int, x:Int): Int = {
  val r = Random.nextInt(6)
  val z = y + (
    if (y>3) 
        -(r%2)
    else if (y<1) 
        (r%2)
    else 
        r/2-1
  )
  buf (z * 30 + x) = '$'
  z
}
(3 /: (0 to 28)(setRowCol (_, _))
println 
buf.mkString ("").sliding(30,30).foreach(println)

My unique invention - well, I haven't read the other solutions so far, is, to generate a Random (6) which is implicitly two Randoms, (2*3). If away from the border, I use the values of r/2 (0,1,2) and → (-1,0,1) tell me, to go up or down. If at the border, I can avoid the character costly call of another random, and just take the modulo(2), to decide, should I stay or should I go.

Let's see the other solutions. :)

#Scala, 211 Bytes

val b=Array.fill(150)('.')
def s(y:Int,x:Int):Int={val r=Random.nextInt(6)
val z=y+(if(y>3)-r%2
else if(y<1)r%2
else r/2-1)
b(z*30+x)='$'
z}
(3/:(0 to 28))(s(_,_))
b.mkString("").sliding(30,30).foreach(println)

sample:

...................$$$...$.$$.
.$$$..............$...$.$.$...
$...$$$..$...$$.$$.....$......
.......$$.$.$..$..............
...........$..................

degolfed:

val buf = List.fill(150)('.').toBuffer
def setRowCol (y:Int, x:Int): Int = {
  val r = Random.nextInt(6)
  val z = y + (
    if (y>3) 
        -(r%2)
    else if (y<1) 
        (r%2)
    else 
        r/2-1
  )
  buf (z * 30 + x) = '$'
  z
}
(3 /: (0 to 28)(setRowCol (_, _))
println 
buf.mkString ("").sliding(30,30).foreach(println)

My unique invention - well, I haven't read the other solutions so far, is, to generate a Random (6) which is implicitly two Randoms, (2*3). If away from the border, I use the values of r/2 (0,1,2) and → (-1,0,1) tell me, to go up or down. If at the border, I can avoid the character costly call of another random, and just take the modulo(2), to decide, should I stay or should I go.

Let's see the other solutions. :)

#Scala, 219 Bytes

val b=List.fill(150)('.').toBuffer
def s(y:Int,x:Int):Int={val r=Random.nextInt(6)
val z=y+(if(y>3)-r%2
else if(y<1)r%2
else r/2-1)
b(z*30+x)='$'
z}
(3/:(0 to 28))(s(_,_))
b.mkString("").sliding(30,30).foreach(println)

sample:

........$$...$$$..............
.......$..$$$...$$........$...
......$...........$...$.$$.$..
$.$..$.............$$$.$....$.
 .$.$$.........................

degolfed:

val buf = List.fill(150)('.').toBuffer
def setRowCol (y:Int, x:Int): Int = {
  val r = Random.nextInt(6)
  val z = y + (
    if (y>3) 
        -(r%2)
    else if (y<1) 
        (r%2)
    else 
        r/2-1
  )
  buf (z * 30 + x) = '$'
  z
}
(3 /: (0 to 28)(setRowCol (_, _))
println 
buf.mkString ("").sliding(30,30).foreach(println)

My unique invention - well, I haven't read the other solutions so far, is, to generate a Random (6) which is implicitly two Randoms, (2*3). If away from the border, I use the values of r/2 (0,1,2) and → (-1,0,1) tell me, to go up or down. If at the border, I can avoid the character costly call of another random, and just take the modulo(2), to decide, should I stay or should I go.

Let's see the other solutions. :)

#Scala, 219 Bytes

val b=List.fill(150)('.').toBuffer
def s(y:Int,x:Int):Int={val r=Random.nextInt(6)
val z=y+(if(y>3)-r%2
else if(y<1)r%2
else r/2-1)
b(z*30+x)='$'
z}
(3/:(0 to 28))(s(_,_))
b.mkString("").sliding(30,30).foreach(println)

sample:

...................$$$...$.$$.
.$$$..............$...$.$.$...
$...$$$..$...$$.$$.....$......
.......$$.$.$..$.............. 
...........$..................

degolfed:

val buf = List.fill(150)('.').toBuffer
def setRowCol (y:Int, x:Int): Int = {
  val r = Random.nextInt(6)
  val z = y + (
    if (y>3) 
        -(r%2)
    else if (y<1) 
        (r%2)
    else 
        r/2-1
  )
  buf (z * 30 + x) = '$'
  z
}
(3 /: (0 to 28)(setRowCol (_, _))
println 
buf.mkString ("").sliding(30,30).foreach(println)

My unique invention - well, I haven't read the other solutions so far, is, to generate a Random (6) which is implicitly two Randoms, (2*3). If away from the border, I use the values of r/2 (0,1,2) and → (-1,0,1) tell me, to go up or down. If at the border, I can avoid the character costly call of another random, and just take the modulo(2), to decide, should I stay or should I go.

Let's see the other solutions. :)