Lorenz attractor&calabi-yau space

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The string theory is believed to take the form of a Calabi–Yau manifold. But the exact shape is not yet known. Is there any possibility that Lorenz attractor equations can define its shape?
 
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Is there any reason to conjecture that it could?
 
There is one simple reason it could not : the dimensions could not match (a Calabi-Yau manifold cannot have a fractal dimension).
 
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