The progression or development of the whole of nature, from the subatomic to the supergalactic, follows this ratio. The twelfth century Italian mathematician, Leonardo P. Fibonacci, observed a predictable sequence of all natural development as shown by a progression of numbers:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ad infinitum.

[1 + 0 = 1] [1 + 1 = 2] [2 + 1 = 3] [3 + 2 = 5] [5 + 3 = 8] [8 + 5 = 13] etc.

The Fibonacci Sequence demonstrates the idea that each stage of natural growth or development refers to its prior state in order to take its next evolutionary step. (This is not unlike Piaget's principle of rapprochement in child psychology.) It also follows the Phi Ratio, e.g. [5 X 1.618 = 8.09] or approximately 8.0, and over the course of the sequence, 1.618... is exact.

The spiral is a common element of Sacred Geometry as well as to all natural development. Spirals in nature tend to follow the Phi Ratio or Fibonacci Sequence in their rates of expansion.

The Sanskrit term mandala roughly translates to "magic circle" or "sacred circle". Mandalas, ancient and modern, frequently offer beautiful examples of radial symmetry and contain elements of Sacred Geometry. They tend to act as activation templates of consciousness. Carl G. Jung studied mandalas from a wide field of world cultures and eras, as well as having advocated for creating our own mandalas as vehicles of soulwork. He noted that when we draw mandalas from the center outward, we tend to process our personal issues or challenges du jour and often gain increased clarity and energy which we can apply to our lives. We are similarly informed simply by gazing at these designs.

The phenomenon of crop circles is also intriguing. These landscape images have been seen for decades, primarily in agricultural regions, yet also in the sands of the Sahara, in arctic snow, and may also be referred to as sand circles or snow circles. Most often, they are found in northern European countries, especially each summer in southwest England in fields of grain and other crops. Since the early 1990's, they've appeared in greatest number, often dozens per season. There has been considerable speculation and controversy concerning their origin, purpose and validity. There has also been the belief that the entire phenomenon has been a hoax, however, it appears that the hoax theory itself is a hoax.*

Among the interesting features of crop circles is that the crops are laid over in such a way that the stalks are not damaged and continue to grow. This seems impossible to replicate with mechanical means or even by hand. Also, the stalks and surrounding soil are electromagnetically altered, as measured with instrumentation.

Crop circles are typically 100 – 200 feet in diameter, although one of 787 foot diameter occurred at Milk Hill in Wiltshire, UK, Aug., 2001. Many of them resemble mandalas. Photograms and images of other shapes have appeared in fields as well and many examples have been aerially photographed. Several elements of Sacred Geometry appear in these designs including Platonic solids, Vesica Pisces, pyramids or tetrahedrons, the Golden Mean and more. Many angles of the designs follow the Phi Ratio. Sometimes the designs are further articulated with apparent reference to our solar system and other star systems as well as a form of hieroglyphics, in a style reminiscent of Egyptian hieroglyphics. The Qabalistic glyph of the Tree of Life has appeared in perfect proportion, as well as symbols from other religious and spiritual traditions. One photogram appeared in Aug., 2001, clearly depicting the Face on Mars, even with a crop line across the face at the same angle which is seen in the Viking (NASA/JPL) photographs of the actual Face on Mars.

Of the myriad explanations of the crop circle phenomenon, one that seems most relevant to me is that of one of my teachers, Bashar, which he offered in a taped, group sharing in the early 1990's. In response to a participant's query, he stated that crop circles are symbolic communication, preparing us for further contact with other beings and other civilizations. Although there has been speculation that these other beings are of extraterrestrial origin, Bashar suggested that many of them are Earth inhabitants, but are extradimensional beings within other dimensions or higher octaves of our dimension. He also suggests that crop circles and crop formations (not necessarily just the circles) are produced through the collective consciousness of these beings and many humans engaged, in certain states of consciousness, in awakening ourselves on a cellular level to higher dimensions of awareness through this symbolic communication.

Fractal images represent the timely marriage between mathematics and computer science. They are often thought of as a new art form as many of them are quite beautiful and inspiring. Among their interesting properties is "self-similarity" or "fractal recursion." This means that if one zooms into any portion of such fractal imagery, infinite design continues to unfold ... similar to peering more deeply into the atom or peering further into deep space.

Prof. Benoit Mandelbrot, a mathematician at Oxford University, discovered a fractal formula in the 1960's, the Mandelbrot Set, which is regarded as one of the classic fractal formulae. Earlier in the 20th century, French mathematician Gaston Julia, discovered a fractal formula referred to as the Julia Set, characterized by spiral patterns which follow the phi ratio and mimic the energy flow in various natural phenomena, including the nautilus, lightning, spiral-armed galaxies, etc. Since their discoveries, numerous fractal equations have been created. These designs often carry elements of Sacred Geometry and communicate to us on many levels, as well as dazzle us with their beauty.

I invite you, if you're so inspired, to peruse the following websites and to draw your own conclusions concerning the myriad connections among these subjects, including their relationship to altered states of consciousness such as NDE.

Related websites on Sacred Geometry can be found here: (01), (02), (03), (04), (05).

Dr. Mandelbrot delivered a lecture at Oxford Univ. in 1991 concerning his discoveries associated with fractal geometry and the Mandelbrot Set. In a slide presentation, he showed several depictions of the Set, including the signature Mandelbrot image. The following morning in a corn field a few miles from the university, a crop circle appeared which perfectly depicted the Mandelbrot image. Local residents were variously concerned, alarmed and intrigued by this development. According to Dr. Chet Snow and other sources, the British Army was called in by the government that morning to burn the field and the design, and a diversionary explanation for the media regarding the occurrence was asserted. This was the birth of the hoax theory which suggested that two Englishmen, known simply as Dave and Doug, had been creating crop circles throughout the English countryside for two decades, using little more that sticks and wooden boards.