No, it is definitely not.That is just plain wrong. Fractal growth patterns are controlled by genetic instructions.
The genome controls protein expression within the cell. That gets translated into cellular differentiation, cell growth, apoptosis, signaling, pigmentation etc. The result is an organism that grows in specific ways. You then see emergent properties like fractal patterns or Fibonacci numbers in the patterns that the organism creates. Nothing in the genome "encodes fractals. "