feat(BNNBot): switch to Gray code encoding for smooth Hamming distance

BNNBot_garage/src/binary_encoding.nim

@@ -14,10 +14,14 @@ type
 
 const MAX_DISTANCE = 1414.0  # diagonal of 1000x1000 arena
 
+proc toGray(value: int): int =
+  value xor (value shr 1)
+
 proc toBits(value: int, bits: int): seq[uint8] =
   result = newSeq[uint8](bits)
+  let gray = toGray(value)
   for i in 0..<bits:
-    result[bits - 1 - i] = uint8((value shr i) and 1)
+    result[bits - 1 - i] = uint8((gray shr i) and 1)
 
 proc encode*(scan: ScanData): BinaryVector =
   var offset = 0