  Chaos is popularly associated with its property of sensitivity to initial
conditions. In this paper we will show that there can be a flip side to this
property which is quite fascinating and highly useful in many applications. As
a result, we can mix a large number of chaotic signals and one completely
arbitrary signal and later a recipient of this transformed and weighted mixture
can separate each of the signals, one by one. The chaotic signals, could be
generated by various maps which belong to the logistic family. The arbitrary
signal, could be a message, some random noise, some periodic signal or a
chaotic signal generated by a source, either belonging or not belonging to the
family. The key behind this procedure is a family of maps which can dovetail
into each other without altering each of their predecessor's symbolic sequence.
