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But I am curious as to your claim that any recursive computation can also be accomplished without recursion. I'm aware of specific cases when this is true , but not of any result to this effect.Jarvis323 said:Anything which can be computed using recursion can be computed without recursion and visa versa. So the question boils down to asking wether all fractals are computable.
I don't know if the definition of a fractal is clear enough to answer. If we are talking about an instance of a fractal then yes, in a trivial way, you can multiply an uncomputable real number with each coordinate value.
Besides a trivial example like that, and if we factor out all of those kinds of non-essential factors like noise, I'm not sure. How about a fractal which switches between two rules periodically as it recurses, but uses an uncomputable sequence to determine if it will switch or not at the start of each period? Then it is morphing unredictably between different fractals. Is that a fractal?