1. Point attractor, such as a pendulum swinging back and forth and eventually stopping at a point. The Attractor may come as a point, in which case, it gives a steady state where no change is made.

2. Periodic attractor, just add a mainspring to the pendulum to compensate for friction and the pendulum now has a limited cycle in its phase space. The periodic attractor portrays processes that repeat themselves.

3. Torus attractor, picture walking on a large doughnut, going over, under and around its outside surface area, circling, but never repeating exactly the same path you went before.  The torus attractor depicts processes that stay in a confined area but wander from place to place in that area. (These first three attractors are not associated with Chaos theory because they are fixed attractors.

4. Strange attractor, this attractor deals with the three-body problem of stability. The strange attractor shows processes that are stable, confined and yet never do the same thing twice.

• Mailing lists
• "the transcendental object at the end of time" - Terence McKenna
• acid rave track _Strange Attractor_ MP3 (160k) by Brainstorm off of _Strange Attractor_ 12" on R&S #037 (1991)
• dark ambient techno track _Strange Attractor_ MP3 (vK) by Exquisite Corpse off of _Dream Night Dance Music_ 12" on Kk #083 (1992)
• track _Strange Attractions_ MP3 (256k) by Tarantel off of _From Bone To Satellite_ on Temporary (1999)
• ambient techno track _Strange Attractor_ MP3 (160k) by Haruomi Hosono with Goh Hotoda, Bill Laswell & Souichi Terada off of _N.D.E._ on Studio Garage, Inc./Antilles (1996)
• ambient breakbeat track _Freeform Attractor (Mixmaster Morris Remix)_ MP3 by Aural Expansion off of _Aural Expansion Remixed Vol. 1_ 12" on SSR #146 (1995)
• track _Dark Attractor_ MP3 by Clock DVA off of _Man Amplified_ CD on Contempo (1992) 

The final crop circle formation of 1997, was the "Strange Attractor" fractal at Hackpen Hill .  The term means "an irreducible invariant set that attracts the trajectories of all nearby points." This term was used by Terence McKenna to describe the "Omega Point," which sucks our evolutionary trajectory towards it, like the plughole at the end of time. 

STANDING STONES AS STRANGE ATTRACTORS - A Speculation
by Jaq. D. Hawkins

The science of chaos is of interest to many magicians. There are several  books in print on the subject, two of which are listed in the sources section at the end of this article.(1)(2) For those who are unfamiliar with the subject, I offer a simplified explanation. In the 1960's and 70's, a few scientists began finding order within the disorder of natural phenomena, such as turbulence in the atmosphere and bodies of water, fluctuations in wildlife population, etc. They were mathematicians, physicists, biologists, chemists, all seeking connections between different types of irregularity.

They used computers to create special kinds of graphic images which capture the delicate structure underlying complexity in nature. They found that order arises spontaneously out of chaotic systems, and simple mathmatical equations are used to model systems every bit as violent as a waterfall. Simple deterministic models could produce what looked like random  behaviour.

A scientist by the name of Edward Lorenz is credited with the discovery of the 'strange attractor', which is a point in phase space which attracts the movements of molecules into spiral patterns. In chaotic systems, the molecules never follow the same path around the attractor, but create a pattern of folds within folds in the pattern, always staying within a limited  range. This can apply to any types of molecule, fluids, gases, or energy.

The original Lorenz attractor moves in a double-spiral pattern around two strange attractors. Other shapes were later created, but the data was always pulled into visible shapes. "Of all the possible pathways of disorder, nature favors just a few."(1)

For many centuries, science has been discovering explanations for things once called magic.(3) It seems reasonable to theorize that our ancestors may have found a way to tap into the natural energy of the earth, depicting their mental images of this energy in diagrams. The inner-folding pathways depicted by the Lorenz diagrams brings to mind the labrinth patterns depicted on the Glastonbury Tor and other sites. The patterns twist within themselves, covering every bit of space within a constricted area, yet the paths never cross. Some of the spiral patterns surrounding a single attractor are reminiscent of the spiral patterns carved on ancient monoliths, known as 'cup and ring' markings.

Scientist and archaeologists have been speculating on the purpose of standing stones and stone circles for many years. Some validity can be found for many theories, the most wisely accepted being for astronomical observation. While this theory seems to fit well with the positioning of the stones erected into circles, it does not explain the individual stones found in a wide variety of situations. Some of these stones have been credited as marking stones for old Roman roads, yet others are found standing in fields or other out of the way locations. These stones are often believed by the local population to have healing properties.  Many people have experienced a "tingling" sensation when they touch the stones, and in some cases a violent rocking sensation that seems very powerful.

The dowser John Williams, feels a representation of a positive and negative force. A Welsh water diviner, Bill Lewis, and John Taylor, professor of mathematics at Kings College, London, made an attempt to measure electromagnetic force on a stone in Crickhowell in South Wales. They used an instrument called a 'gaussmeter', which is used to measure static magnetic field strength. A young Argentinian physicist, Dr. Eduardo Balanovski, went along to see if there was anything odd about the stone. When he pointed the meter to the stone, the needle shot up to capacity. Not only did the stone have a measurable energy field, but the strength could be measured in bands around the stone. Possibly a spiral?  There has not been enough 'proper' scientific research on this subject to draw any hard conclusions, but the evidence seems to point to these stones somehow acting as amplifiers for natural energy currents within the earth.   There is some evidence that these stones are placed above points where two or more underground streams cross. Water moving through an underground tunnel creates a small electric charge. The charge is stronger  where  these streams cross. Keeping in mind the spiral patterns of turbulence, now measurable by chaos science methods, the theory exists that the stones are charged by this hydroelectric reaction. The molecular structure of quartz is spiral, and quartz seems to be a constituent of every 'active' stone. Coincidence?

Modern man is always eager to believe that our ancestors were primative animals, with nothing more important to think about than their next meal, but the evidence is increasingly pointing to a different picture. One where our
ancestors had architectural and building skills, mathematical and astronomical knowledge.   The next obvious step is to discover a way to use this energy spiraling around the stone. What did our ancestors use it for? The answer is yet to be discovered.

Sources:
(1) _CHAOS, making a new science_   by James Gleick
(2) "TURBULENT MIRROR" by John Briggs & F. David Peat
(3) "EARTH MAGIC" by Francis Hitching

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