Implement trace functionality for Hopfield and Hamming networks; update Gemfile.lock and app.rb for new dependencies and features

trace.rb

@@ -0,0 +1,18 @@
+def trace_hopfield_step(weights, vector)
+  n = vector.length
+  Array.new(n) { |i| n.times.sum { |j| weights[i][j] * vector[j] } }
+end
+
+def hamming_trace(pattern_vectors, input_vec)
+  n = input_vec.length
+  k = pattern_vectors.length
+  dots = pattern_vectors.map { |pv| pv.zip(input_vec).sum { |a, b| a * b } }
+  initial = dots.map { |dot| (dot.to_f + n) / 2.0 }
+  {
+    eps:             (0.9 / k).round(6),
+    k:               k,
+    n:               n,
+    dot_products:    dots,
+    initial_outputs: initial.map { |v| v.round(2) }
+  }
+end