Not sure how you were supposed to get all that from the logo. Do you need to have all that colplexity? Why not just have 'Rogue Wave' as the logo? Or if the logo will always be acompanied by the name of the business do you need the R and W in the logo.
It just seems overly complicated and abstruse.
PS: The butterfly effect is part of chaos theory. It's the dependence of initial conditions on non-linear events. I did this as part of my degree and it's enormously complicated. Rogue waves aren't necessarily dependent on initial conditions. They are more often the result of resonance. So linking the butterfly effect to rogue waves doesn't actually work.