Logarithmic spiral

Spiral types

The systems view of life, not surprisingly, includes a new systemic understanding of evolution. Rather than seeing evolution as the result of only random mutations and natural selection, we are beginning to recognize the creative unfolding of life in forms of ever-increasing diversity and complexity as an inherent characteristic of all living systems. Although mutation and natural selection are still acknowledged as important aspects of biological evolution, the central focus is on…

Recently I have been working a lot on fractal programming, here are a few examples (just click the images to view their respective articles)...

Phi, or 1.618, is known as the golden ratio, and can be found throughout artistic composition and nature. It can be represented in the formula (a+b)/a = a/b = phi.This formula applies to the golden…

The logarithmic spiral of the chambered Nautilus shell.

You've seen logarithmic spirals, but here's the Spiral Logarithm! It has its radial distance to the origin equal to the (offset) logarithm of its arc-length: r = log(s+1). Pictured log base 2. I came up with this the other day, but didn't find it being constructed elsewhere.

“https://t.co/2Wyx1rErA5”

Anita Chowdry. Alternative shamsa / Fibonacci spiral

Illustration showing succession of golden rectangles that are used to construct the golden spiral. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. Each rectangle shown is subdivided into smaller golden rectangles. The golden spiral is a special type of logarithmic spiral. Each part is similar to smaller and larger parts.

The «spira mirabilis» (wonderful spiral) is a particular logarithmic spiral described for the first time by René Descartes and subsequently paid attention to by the Swiss mathematician and scientist Jakob Bernoulli, whose curve wraps around the pole without however ever reaching the starting point. Its peculiarity lies in the fact that the spiral has neither beginning nor end and, despite the infinite evolutions and rotations, always remains similar to itself. Bernoulli's adjective…