Fibonacci Sequence!

[DennisK]

I am upset that I was never taught about the Fibonacci Sequence, Mandelbrot Set or other fractals in high school or college.  These things should be taught at an early age because of the mere potential for stimulating thought on so many levels.  I had never heard of these concepts except for fractals (but only a smidgeon).  For my little brain at least, it is mind blowing finding the Fibonacci Sequence in nature.  Not only the spiral usually associated with Fibonacci design, but the numbers 1,1,2,3,5,8,13... being repeated in nature (e.g.,family tree of honeybees http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#bees or the human body) or the sequence being shown in man made phenomena like the stock market http://goldennumber.net/stocks.htm

Please list your experience with the Fibonacci Sequence, Mandelbrot Set or fractals along with any insights you have.

[Will]

Fibonacci was my entrance to an understanding of fractals. I'll admit that I've forgotten more about math in the past few years than most people ever learn, but I do remember my fascination with the amazing patterns that come about in mathematics. There's something almost peaceful about the perfect system of maths. Everything follows a rule, and every rule makes perfect sense.

[4DeepThought2]

I was taught the Fibonacci Sequence last year by my math teacher the last day of school, hence my forgetfulness of it. I remember the discussion of the relation between the sequence and nature, which is quite interesting. I know little of the subject and am wondering if there is a scientific explanation as to why this sequence appears in nature so often?

[DennisK]

I was taught the Fibonacci Sequence last year by my math teacher the last day of school, hence my forgetfulness of it. I remember the discussion of the relation between the sequence and nature, which is quite interesting. I know little of the subject and am wondering if there is a scientific explanation as to why this sequence appears in nature so often?

This link touches upon Fibonacci Sequence in nature, but it doesn't say why. http://www.world-mysteries.com/sci_17.htm#Nature

I haven't been able to find any explanations as to why.  God works in mysterious ways?   Seriously, though, regardless of what the interpretations may be as to "why", the relationship to math, cosmology, biology, botony, physics, etc. are fascinating and should be integral in the teachings in school at all levels.  I realize we cannot explain the Fubinacci Sequence, but that doesn't mean we should shield minds from it by not teaching it in-depth.  There is an undeniable link and exposing more minds to it can only bring clarity, or at the very least, more understanding.  Even if it gets kids no closer to an answer, it can explode thought on so many levels.  It may inspire millions of kids to think vs. being complacent and taking someone's word for anything.

[curiosityandthecat]

[SSY]

the why part is some function of the organism, With regards to the fibonacci sequence, let us imagine the growth of some organism. Parts of this organism die after two after 2 hours. the growth of the rest of the organism is proportioanl to the total size of the organism at that time.

start at size one, after an hour, have produced another unit of size 1.

at the start of the second hour, have size of 2 units, so in the second hour, it will produce 2 units of growth.

at the start of the third hour, the first unit dies, total organism size is now three, so produces three units this hour

at the start of the fourth, the second unit dies, total size now 5 units, 5 untis growth

fifth hour, the double unit does, total size now 8, 8units of growth

etc etc.

the above example is artificial, but similar mechanism happen in cascades of chemical release, where the amount of chemical released is proportional to the amount of chemical present, and the chemical has some half life similar in length to the time taken to release more chemical.

the logarthmic sequence apears in animals for the same reason, one example being the nautilus shell, where each segment is a facto bigger than the last, as the bigger the nautilus, the faster it can add mass to its shell.

[DennisK]

the why part is some function of the organism, With regards to the fibonacci sequence, let us imagine the growth of some organism. Parts of this organism die after two after 2 hours. the growth of the rest of the organism is proportioanl to the total size of the organism at that time.

start at size one, after an hour, have produced another unit of size 1.

at the start of the second hour, have size of 2 units, so in the second hour, it will produce 2 units of growth.

at the start of the third hour, the first unit dies, total organism size is now three, so produces three units this hour

at the start of the fourth, the second unit dies, total size now 5 units, 5 untis growth

fifth hour, the double unit does, total size now 8, 8units of growth

etc etc.

the above example is artificial, but similar mechanism happen in cascades of chemical release, where the amount of chemical released is proportional to the amount of chemical present, and the chemical has some half life similar in length to the time taken to release more chemical.

the logarthmic sequence apears in animals for the same reason, one example being the nautilus shell, where each segment is a facto bigger than the last, as the bigger the nautilus, the faster it can add mass to its shell.

I'm not getting the "why" explanation.

[SSY]

In one sentance, it would be

The size of the organism determines the rate of growth, meaning a larger organism grows faster.

[curiosityandthecat]

Think of it like making money. If you make minimum wage, it's hard to turn that money into a very large sum. Conversely, if you make $100,000 a year, it's very easy to turn that into an extremely large amount of money.

[DennisK]

In one sentance, it would be

The size of the organism determines the rate of growth, meaning a larger organism grows faster.

I understand this concept, but it's still not telling me why nature follows this sequence.  Or why there's a relationship to the curvature of a ram's horns or a nautilus. Or why there's a relationship to Pascal's triangle.  Forgive me.  I believe myself to be in a similar mode of just learning about all of Santa's magical intricacies.  Therefore, I may not be able to see the forest for the trees.