Spiral waves in colonies of the mold Dictyostelium discoideum.
Alan Turing was the first one who proposed reaction-diffusion systems as a theoretical idea to explain biological morphogenesis. It demonstrates how breaking and pattern formation can arise out of a homogeneous, uniform state.
The Belousov-Zhabotinsky reaction is a special non-equilibrium system that works as a chemical oscillator as it cycles through its different states in autocatalytic fashion. If unmixed the diffusing chemicals spread and cause spirals to emerge and grow.
While most 13-year-olds spend their free time playing video games or cruising Facebook, one 7th grader was trekking through the woods uncovering a mystery of science. After studying how trees branch in a very specific way, Aidan Dwyer created a solar cell tree that produces 20-50% more power than a uniform array of photovoltaic panels. His impressive results show that using a specific formula for distributing solar cells can drastically improve energy generation. The study earned Aidan a provisional U.S patent – it’s a rare find in the field of technology and a fantastic example of how biomimicry can drastically improve design.
Aidan Dwyer took a hike through the trees last winter and took notice of patterns in the mangle of branches. His studies into how they branch in very specific ways lead him to a central guiding formula, the Fibonacci sequence. Take a number, add it to the number before it in a sequence like 1+1=2 then 2+1=3 then 3+2=5, 8, 13, 21 and so on a very specific pattern emerges. Turns out the pattern and its corresponding ratios are reflected in nature all the time, and Aidan’s keen observation of how trees branch according to the formula lead him to test the theory. First he measured tree branches by how often they branch and at what degree from each other.
To see why they branch this way he built a small solar array using the Fibonacci formula, stepping cells at specific intervals and heights. He then compared the energy output with identical cells set in a row. Aidan reports the results: “The Fibonacci tree design performed better than the flat-panel model. The tree design made 20% more electricity and collected 2 1/2 more hours of sunlight during the day. But the most interesting results were in December, when the Sun was at its lowest point in the sky. The tree design made 50% more electricity, and the collection time of sunlight was up to 50% longer!”
His results did turn out to be incorrect though. Voltage (what he measured) is not an accurate measure of energy from a solar cell– he measured higher voltage simply because he swept a larger portion of sky. Solar cells in series are as only as good as the weakest one, so the tree design is only as good as the worst positioned cell for amperage, which multiplied by voltage creates usable energy.
This story is very inspiring and I think that Aiden’s passion to unravel a mystery shows how exciting the path of scientific discovery is. Impressively he is demonstrating the power of biomimicry — a concept that many see as the pinnacle of good design, but one that thus far has been exceptionally difficult to achieve. Way to go!
Carol Prusa, Hyperstrings
“Macro and micro scales collide in intimate exchanges. The chaotic abyss rebounds. All states are becoming and disintegrating.”
Believed to be the most geometrically complex and aesthetically beautiful structure in mathematics, the 421 polytope is the algebraic form at the centre of a universal theory of everything. Originally described in the late 19th century, 421 models all interactions and transformations between known and postulated sub-atomic particles. The theory is an attempt to reconcile one of the fundamental unsolved problems in physics: unify quantum physics and gravitation in hopes of ultimately explaining the fabric of the universe.
The visualization was hand drawn in Illustrator to an accuracy of 1/10,000 of a millimeter. The poster is a minimalistic composition focused on the accurate representation of the 421 polytope and can be ordered on Peter’s website. The sophisticated print consists of silk screen print matte black on glass clear plastic with hand-applied 23 carat rouge gold foil and gold powder gilding.
Sacred geometry asserts that by analyzing and working with geometric figures, one attunes to the mystical laws of creation. Geometry is an important part of energy healing because subtle energies often organize in shape and form. Because of this, healers throughout history have employed symbols by using psychic visioning and by constructing healing instruments in various shapes. Geometry is also interrelated with sound.
Geometric theories began emerging thousands of years ago, most notably during the time of Plato and his predecessor, Pythagorus. The geometric proportions developed during this time period have been used by most civilizations since and applied to mathematics, art, architecture, cosmology, music, astronomy, and physics. Here are a few applications of sacred geometry to healing and energy.
BASIC GEOMETRY THEORIES
There are several geometry theories that apply to healing energies.
The applications of these shapes to music are important to sound healing theory. The ancients have always professed a belief in the “music of the spheres”, a vibrational ordering to the universe. Pythagorus is famous for interconnecting geometry and math to music. His music ratios were seen as forming harmonics that could restore a disharmonic body – or heal. Huns Jenny furthered this work through the study of cymatics, and contemporary sound healer and author Jonathan Goldmanconsiders the proportions of the body to relate to the golden mean. Geometry also seems to serve as an ‘interdimensional glue,’ according to a relatively new theory called causal dynamical triangulation (CDT). According to CDT, time-space is divided into tiny triangulated pieces, with the building block being a pentachoron. Each simple, triangulated piece is geometrically flat, but they are glued together to create curved time-spaces. Many of these forms are geometrical in nature.
Cymatics studies that different frequencies produce different patterning effects. The nature of these patterns at least partially depends on spin, the rotation around a central axis that determines the resulting movements. In his book Mind, Body and Electromagnetism, author John Evans shows that there are various patterns produced by frequency and spin in the human body. He suggests that the cellular material of the body is patterned by electromagnetic waveforms with an ordering of frequency along the central axis. A simple change alters the vibrational qualities of the object and therefore its effects. And this is the basis of energy healing – changing frequency or spin through field dynamics.
— Cyndi Dale, The Subtle Body
Revisting one of my favorite books. Thanks to Lands of Wisdom for conveniently posting this excerpt.
The Sacred Circle
A plain black circle was to symbolize the spirit of the solar or heavenly god during his cyclic passages through the underworld. In this phase, according to Egyptian scriptures, he became “the hidden one” (Amen), or the Lord of Death, Seker, hidden in a secret pyramid of “blackest darkness” at the earth’s core. His blackness was as intensely dark as the suns light was intensely bright. He soon became mythologized as the sun god’s dark twin brother, like Ahriman to Ahura Mazda in Persia, or Nehral-Ninib to Anu in Mesopotamia.
The dark brother became an opponent of the bright brother with further development of dualism, which divided the world between forces of light and dark (good and evil). Thus the Black Sun came to symbolize many underworld gods, including: Saturn, Pluto, Hades, Python, Apollyon, Zeus Chthonios, Yama, and such fallen-angel figures as Lucifer, Satan or Beelzebub who became assimilated to the Christian devil.
Yet all the while, the sun continued to rise and decline in the sky hourly, daily, and yearly. Seeing this, many people retained the original idea of the Black Sun as a secret, wiser version of the solar god, who knew the nether world as well as he knew the heavens.
To medieval alchemists, the Sol Niger (Black Sun) meant “prime matter,” or matter in an untouched primordial state.
The circle was always one of the primary feminine signs, as opposed to the line, cross, or phallic shaft representing masculine spirit. Early matrifocal villages had round hearths, round houses, round fences and defensive shapes. The cirlce was associated with the idea of a protected or consecrated space, the center of the motherland, a ceremonial space where all participants were equal. Worship circles like the Hindu chakra were those in which female influence was prevalent. Pagan sacred dances were circular, as are European folk dances to this day. Prehistoric stone circles, like Stonehenge-known as the Giant’s Dance-attest to ancient love of circularity. The concept of equality was still connected with the circle in medieval legends. Arthur’s knights of the Round Table were seated in a circle to eliminate the sense of hierarchy among their brotherhood.
The famous cliche, “God is a circle whose circumfrence is nowhere and whose center is everywhere,” was cribbed from a Hindu catechism concerning the deity called the One: “an unbroken circle with no circumfrence, for it is nowhere and everywhere.” The idea of the cosmos as an unbroken circle was repeated in the Gnostic image of the world serpent forming a circle with its tail in its mouth. Closed circles continued to be thought protective, especially for workers of magic. A sorcerer’s title dating from the first century B.C. was “circle drawer.” The circle invoked by analogy the full face of the moon, the pupil of the All-Seeing Eye, the circle of the visible horizon, and a thousand other natural forms.
— Barbara Walker, The Woman’s Dictionary of Symbols & Sacred Objects
Seen a few works by this artist but still wondering who it is…
Hang on tight while we grab the next page