fibonacci spiral


isometrica_minerals Halite with Tolbachite with natural Fibonacci spiral growth habit from the Sieroszowice Mine, Lubin, Legnica, lower Silesia, Poland. This remarkable piece was the only one from this pieces I saw from this production with this unusual spiral characteristic. Definitely drew awe from me. 


Geometry at work: Orbital Resonance, Sound and Water

Richard Proctor, Old and New Astronomy, 1892

What men recognized then in the movements of the heavenly bodies is true now and true for all time. And even in dealing with the limited knowledge and the imperfect methods of ancient astronomers, we need not hesitate to consider these movements as they are now recognized and understood.

Ernst Chladni, Die Akustic, 1802

Nodal lines of vibrating circular or polygonal  plates, according to Chladni and Savart.The breakthrough work acquired a status of foundational work of a new scientific field and earned him a title of “father of acoustics”. It was the first systematic description of the vibrations of elastic bodies.

Snowflake Man

Wilson Alwyn “Snowflake” Bentley (February 7, 1865 – December 23, 1931), is one of the first known photographers of snowflakes. He perfected a process of catching flakes on black velvet in such a way that their images could be captured before they either melted or sublimated.


Geometry at work: Sea animals, Fruits and Vegetables and Plants

The Nautilus

The nautilus (from the Latin form of the original Ancient Greek ναυτίλος, ‘sailor’) is a pelagic marine mollusc. Although not a golden spiral, the nautilus shell presents one of the finest natural examples of a logarithmic spiral.

Geometry of fruits and vegetables

When sliced in half, the majority of the depicted fruits and vegetables will display a geometric shape or pattern, based on symmetry or platonic solids.

The arrangement of leaves

Phyllotactic spirals form a distinctive class of patterns in nature, depicting the  arrangement of leaves on a plant stem.
The basic patterns are alternate, opposite, whorled or spiral, many of them arranged based on consecutive fibonacci numbers.

Analysis of the Julia Set crop circle

As most of us can discern, the formation of July 7 1996 that appeared across the road from Stonehenge in Wiltshire UK clearly represents the Fibonacci sequence, or the sacred spiral. It also accurately represents the fractal known as Julia Set, hence the name. Fibonacci is a very important mathematical phenomena which shows itself in many forms of nature (spiral galaxies, spiral seashells, plants, etc). The formation appeared within the time window of 45 minutes in broad daylight next to a very busy highway and Stonehenge, which has 24 hour surveillance. No one was seen making this formation. Read more about that here.

Fibonacci has also been attributed to have spiritual/metaphysical concepts embedded within it, and thus, shows itself in many forms of nature around us. It is believed that Fibonacci represents the sacred spiraling, never-ending nature of the entire Universe and our internal spirit. Spirals have commonly been viewed as sacred symbols in many ancient societies.

It is also commonly believed that the Universe formed from one point - the singularity - and spiraled outward and continued to expand bringing forth all of creation. My analysis of the formation led me to the conclusion that the center circle represents the singularity or source from which all creation originates and the spiral representing creation itself. The circle itself also represents the all-encompassing wholeness of the Universe, meaning that all things are interconnected. The concept represents both spiritual and scientific principals.

The sequels of the single Julia Set (Triple, 1996 & Double Triple, 2001) seem to represent the same concept, but on a grander scale. It makes sense, to me, that the circle makers are trying to convey the communication of both the spiritual and scientific concepts of the Universe in order for us to understand the interconnected nature of ourselves and reality. What a beautiful message it truly is.


Fibonacci Sculptures - Part II

These are 3-D printed sculptures designed to animate when spun under a strobe light. The placement of the appendages is determined by the same method nature uses in pinecones and sunflowers. The rotation speed is synchronized to the strobe so that one flash occurs every time the sculpture turns 137.5º—the golden angle. If you count the number of spirals on any of these sculptures you will find that they are always Fibonacci numbers.

© John Edmark