It's seldom that I have opportunities to go Full Tilt Nerd. Imagine the squee! when I saw the BBC's Science Focus magazine's "What is the Fibonacci Sequence?" article.
"Flowers, pine cones, shells, fruits, hurricanes
and even spiral galaxies, all exhibit the Fibonacci sequence."
I have a fractal-loving cousin who doesn't get into the math itself. How it looks vs why it works at all, I suppose? The Fibonacci sequence is a fractal sequence and fractals are repeated geometric objects. Confusing? Yes.
At the sequence's core is this simple concept:
Fibonacci Sequence is portrayed in that familiar snail shell pattern, aka the Golden Spiral. The Rule is xn = xn-1 + xn-2
Rinse and repeat.
Joe Wezorek (MIT god and all-around decent mathematical badass) explains it best:
"The fibonacci sequence does have a natural recursive definition, a common trait of many fractals, and this definition leads to visualizations of the fibonacci sequence that do exhibit self-similarity.
"For example, the pseudo-logarithmic spiral consisting of circular arcs embedded in fibo(n) sized squares
but I would not really characterize the above as a fractal for the same reasons I wouldn't characterize the regular square lattice as a fractal even though it also exhibits self-similarity. This all comes down to one's definition of the word "fractal" so your mileage may vary.
"Off the top of my head, the only "real" fractal that I know of that is related to the fibonacci series is a construction that can be made by interpreting fibonacci words
as turtle graphics commands, i.e. as an L-system,
which is related to the fibonacci sequence in various, interesting, ways.
I had no intention to teach anybody anything today. Just opening my mind's door and pushing away cobwebs, thanks to Science Focus.
Here's a cute bunny to brighten your day.
