Fibonacci spirals
I did some research to try to clarify what exactly was up with Fibonacci.
There is a Golden rectangle, which I learned about without ever hearing of Fibonacci. There is a Fibonacci spiral and a Golden spiral. Here's what I have gathered from Wikipedia.
By definition, the first two Fibonacci numbers are 0 and 1, and each subsequent number is the sum of the previous two. 0 1 1 2 3 5 8 13 21 34, easy right?
And that will result in this rectangle.
A Fibonacci spiral is not a true logarithmic spiral. Every quarter turn a Fibonacci spiral gets wider not by phi, but by a changing factor related to the ratios of consecutive terms in the Fibonacci sequence. The ratios of consecutive terms in the Fibonacci series approach phi, so that the two spirals are very similar in appearance. The golden spiral turns would be related directly to phi., not so easy right?
The Golden spiral is a true logarithmic spiral and is visually almost exactly the same.
Here is the golden rectangle which is easy to make with a compass and ruler. Draw a square (red lines). Draw a line from the middle of one side to a corner. This line is the radius of a circle -draw the circle. The rectangle is formed.
This results in a rectangle slightly different than what digital or even 35mm offers. An old 35mm negative was 1:1.5, the Fibonacci format is 1:1.6 and the current digital format is 1:1.3. Why is this important? It totally affects the composition and the format is purported to be more aesthetically pleasing.
Easy, huh? Now use this rectangle and its proportions as the format for presenting images of spirals, thus the 'Fibonacci Spiral Series'.
There is a Golden rectangle, which I learned about without ever hearing of Fibonacci. There is a Fibonacci spiral and a Golden spiral. Here's what I have gathered from Wikipedia.
By definition, the first two Fibonacci numbers are 0 and 1, and each subsequent number is the sum of the previous two. 0 1 1 2 3 5 8 13 21 34, easy right?
And that will result in this rectangle.
A Fibonacci spiral is not a true logarithmic spiral. Every quarter turn a Fibonacci spiral gets wider not by phi, but by a changing factor related to the ratios of consecutive terms in the Fibonacci sequence. The ratios of consecutive terms in the Fibonacci series approach phi, so that the two spirals are very similar in appearance. The golden spiral turns would be related directly to phi., not so easy right?
The Golden spiral is a true logarithmic spiral and is visually almost exactly the same.
Here is the golden rectangle which is easy to make with a compass and ruler. Draw a square (red lines). Draw a line from the middle of one side to a corner. This line is the radius of a circle -draw the circle. The rectangle is formed.
This results in a rectangle slightly different than what digital or even 35mm offers. An old 35mm negative was 1:1.5, the Fibonacci format is 1:1.6 and the current digital format is 1:1.3. Why is this important? It totally affects the composition and the format is purported to be more aesthetically pleasing.
Easy, huh? Now use this rectangle and its proportions as the format for presenting images of spirals, thus the 'Fibonacci Spiral Series'.
posted by bZed at 7:35 PM
2 Comments:
Good clarification Dave
If you google PHI you will find some very interesting facts about this number.
This site tells you how beautiful you are by using the 1.6:1 ratio to measure your face. http://www.beautyanalysis.com/index2_mba.htm. We instinctively recognize this ratio as beautiful and seek it out. Why this number shows up repeatedly in nature is an interesting mystery. I love fun with numbers
I love fun with numbers too. I had heard about the 'Beauty Mask" a few years back but didn't know it was based on Phi, cool! Looks like my face is a little too long, damn, my illusion is shattered. lol
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