Based on the research conducted so far, I have refined my original idea about replicating dimensions. The original idea consisted of multiple dimensions existing in various parts of the universe. Since the universe is so vast and continues to grow, these "dimensions" might be governed by different laws of physics.
Then came the concept of multiple dimensions existing in one universe/one timeline, similar to multiple carts connected on a railroad track. The idea of jumping from one cart to another is analagous to time traveling from one dimension to another. This eliminates the contradiction/paradox that if one were to travel back in time and kill his father, one would not exist.
Finally, thanks to string theory, I have a much better understanding of what our universe is actually like. Every bit of matter or force is made of tiny vibrating strands of energy called strings. This theory predicts that there are a grand total of eleven dimensions. These dimensions determine how the forces and matter look like for a particular universe. This means that there are other parallel universes which contain other possible outcomes of all events that ever happened. These universes may even be governed by different laws of physics depending on the way the strings in that universe vibrate in the eleven dimensions.
For our particular universe, we may change our lives by traveling through the fourth dimension (time) to the past and triggering events that will lead to a different outcome. Another way to reach a different outcome/life is to go through the fifth dimension. However, since we are on the verge of completing the time machine, we may use it to travel to the fourth dimension and change things around. This process of repeating your life, perhaps in a different way than you have lived, is what I mean by "self-replicating". The habitat that is associated with this concept is, the fourth dimension - time.
In order to illustrate such a concept, I intend to construct a few drawings to model the act of reproducing one's life. In addition to these drawings, I feel that producing a video of some sort using the equipment we have might give us all a better understanding of the concept I have.