The Fibonacci sequence
The Golden spiral should be created drawing circular arcs connecting the opposite corners of the squares in the Fibonacci multi square tiling. In fact, this should be considered an "approximate "golden spiral. As you can see here, the black spiral used on this drawing with a continues curvature, since the circular arcs give us some discontinuity perception. Anyway, this is to another rough approximation to a true golden logarithmic spiral using the illustrator Bezier curves.
The Rule of Thirds
Most standard-sized canvases have a length, the width ratio of between 1.2 and 1.4 to 1 somewhat shorter than the ideal golden ratio of 1.618: 1. A 12 x 16 canvas, for instance, is 1.33. 1. on these formats, the "sweet spot" (shown below in red) fall very close to the lines dividing the sides into thirds (shown in blue). This has led to a simplification of the golden ratio principle, known as the Rule of Thirds, which approximates the "sweet spot" by dividing each edge of the canvas into thirds.
I understand the Rule, a simplified version of the golden mean, where the frame is divided into nine sections and the points that naturally, attracts interest of the viewer, this is where the intersections is the lines that cross each other. I have struggled somewhat with the "sweet spot" because there seem to be so many different understandings of it.
The Fibonacci series can be found in flower petals, seed heads, and leaf and branch arrangements on trees, even fallen ones, and the spirals can be found in shells fossilized or living, even vegetables like cauliflower, on butterflies wings, dolphins, the solar system. The list is endless and can just about be applied to anything even the human body.
I appreciate that the balance of these compositions looks attractive, although there is a lot of room for me to improvement. I found the theory of the "sweet spot" quite a task to grasp, however, translating that information into a photograph I found a little easier. Generally though this has been the most enjoyable section for me as I like pictures, and I think that I have probably spent far too long looking at all the ones out there. (Knott, D. R.)
The Golden spiral should be created drawing circular arcs connecting the opposite corners of the squares in the Fibonacci multi square tiling. In fact, this should be considered an "approximate "golden spiral. As you can see here, the black spiral used on this drawing with a continues curvature, since the circular arcs give us some discontinuity perception. Anyway, this is to another rough approximation to a true golden logarithmic spiral using the illustrator Bezier curves.
The Rule of Thirds
Most standard-sized canvases have a length, the width ratio of between 1.2 and 1.4 to 1 somewhat shorter than the ideal golden ratio of 1.618: 1. A 12 x 16 canvas, for instance, is 1.33. 1. on these formats, the "sweet spot" (shown below in red) fall very close to the lines dividing the sides into thirds (shown in blue). This has led to a simplification of the golden ratio principle, known as the Rule of Thirds, which approximates the "sweet spot" by dividing each edge of the canvas into thirds.
I understand the Rule, a simplified version of the golden mean, where the frame is divided into nine sections and the points that naturally, attracts interest of the viewer, this is where the intersections is the lines that cross each other. I have struggled somewhat with the "sweet spot" because there seem to be so many different understandings of it.
The Fibonacci series can be found in flower petals, seed heads, and leaf and branch arrangements on trees, even fallen ones, and the spirals can be found in shells fossilized or living, even vegetables like cauliflower, on butterflies wings, dolphins, the solar system. The list is endless and can just about be applied to anything even the human body.
I appreciate that the balance of these compositions looks attractive, although there is a lot of room for me to improvement. I found the theory of the "sweet spot" quite a task to grasp, however, translating that information into a photograph I found a little easier. Generally though this has been the most enjoyable section for me as I like pictures, and I think that I have probably spent far too long looking at all the ones out there. (Knott, D. R.)
Bibliography
Knott, D. R. (1996/2011, March Tuesday).
maths.surrey.ac.uk. Retrieved November sunday, 2011, from Fibonacci Numbers and the "sweet spot" : http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/
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