  Fixed point iterations are known to generate chaos, for some values in their
parameter range. It is an established fact that Turing Machines are fixed point
iterations. However, as these Machines operate in integer space, the standard
notions of a chaotic system is not readily applicable for them. Changing the
state space of Turing Machines from integer to rational space, the condition
for chaotic dynamics can be suitably established, as presented in the current
paper. Further it is deduced that, given random input, computation performed by
a Universal Turing Machine would be 'almost surely' chaotic.
