[en] We construct a model of the RNA world in terms of naturally evolving nucleotide sequences assuming only Crick-Watson base pairing and self-cleaving/splicing capability. These sequences have the following properties. 1) They are recognizable by an automation (or automata). That is, to each k-sequence, there exist a k-automation which accepts, recognizes or generates the k-sequence. These are known as automatic sequences. Fibonacci and Morse-Thue sequences are the most natural outcome of pre-biotic chemical conditions. 2) Infinite (resp. large) sequences are self-similar (resp. nearly self-similar) under certain rewrite rules and consequently give rise to fractal (resp.fractal-like) structures. Computationally, such sequences can also be generated by their corresponding deterministic parallel re-write system, known as a DOL system. The self-similar sequences are fixed points of their respective rewrite rules. Some of these automatic sequences have the capability that they can read or 'accept' other sequences while others can detect errors and trigger error-correcting mechanisms. They can be enlarged and have block and/or palindrome structure. Linear recurring sequences such as Fibonacci sequence are simply Feed-back Shift Registers, a well know model of information processing machines. We show that a mutation of any rewrite rule can cause a combinatorial explosion of error and relates this to oncogenetical behavior. On the other hand, a mutation of sequences that are not rewrite rules, leads to normal evolutionary change. Known experimental results support our hypothesis. (author). Refs