: any of various extremely irregular curves or shapes for which any suitably chosen part is similar in shape to a given larger or smaller part when magnified or reduced to the same size



Fractal (n.): “never-ending pattern,” 1975, from French fractal, from Latin fractusinterrupted, irregular,” literally “broken,” past participle of frangereto break” (related to: fraction). Coined by French mathematician Benoit Mandelbrot (1924-2010) in “Les Objets Fractals.”

“Many important spatial patterns of Nature are either irregular or fragmented to such an extreme degree that… classical geometry … is hardly of any help in describing their form … I hope to show that it is possible in many cases to remedy this absence of geometric representation by using a family of shapes I propose to call fractals – or fractal sets.” [Mandelbrot, “Fractals,” 1977]



“Why is geometry often described as ‘cold’ and ‘dry?’ One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.”

Benoit B. Mandelbrot (1924-2010, Polish-born, French and American mathematician, known as the “father of fractals,” which may describe diverse behaviors in economics, finance, the stock market, astronomy, and computer science.)

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“At other times I wake up from the half sleep I'd fallen into, and hazy images with poetical and unpredictable colours play out their silent show to my inattention.”

Fernando Pessoa (1888-1935, Portuguese poet, writer, literary critic, translator, publisher, and philosopher; he was known for taking on 72 individualized literary personas and authorships, known as heteronyms.)

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“All high mathematics serves to do is to beget higher mathematics.”

Ashim Shanker (poet, philosopher, writer and author of Don’t Forget to Breathe)

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“Cocoa-buttered girls were stretched out on the public beach in apparently random alignments, but maybe if a weather satellite zoomed in on one of those bodies and then zoomed back out, the photos would show the curving beach itself was another woman, a fractal image made up of the particulate sunbathers. All the beaches pressed together might form female landmasses, female continents, female planets and galaxies. No wonder men felt tense.”

Bonnie Jo Campbell (b. 1962, American novelist and short story writer, and 2011 Guggenheim Fellow; most recent work is: Mothers, Tell Your Daughters)

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“…a higher consciousness of love, compassion, high-minded thinking, integrity and caring … creates multiple fractals. It creates a confluence of energy that then creates more of itself in the way of harmonics of itself [many more fractals of higher frequencies that are specific multiples of the original]. These fractal waves emanate outward, enhancing that which is around it in a never-ending cycle. It's expansive; it's catchy [additive]; it's structured in a complex fashion; and the harmonics create other fractals way beyond their own scope. It has an influence with other matter everywhere.”

Lee Carroll (spiritual teacher and metaphysical channel for Kryon, for whom he presented his message of love to the delegates and guests of the Society for Enlightenment and Transformation at the United Nations in 1995, 1996, 1998, 2005, and 2006)

Bio Source:


“All high mathematics serves to do is to beget higher mathematics.”

— Ashim Shanker

What if we could create cosmic wonders in the smallest of our deeds?  What ways could we instigate such miracles?

What if we could shift our world towards peace through kindness and by connecting to strangers in meaningful ways, would we have the courage to do so?

What if we could rewire our brains and expand the capacities of our mind by stepping out of our comfort zones by partnering and collaborating with those that have opinions that differ from our own?

What if we could travel around the world just by walking outside our door and introducing ourselves to our neighbors? Could we fully explore outside our familiar radius?

Could we open our homes or visit someone we always wanted know, and talk honestly about our thoughts on such taboo subjects like religion, race, ethnicity, politics, and sex?  Could we do so with sincere compassion, respect, and love?  Could we be playful instead resistant?

Do we have the courage to look a fellow traveler directly in the eyes and face our own reflections?  In doing so, we are breaking off from the norm and forging original thinking and original action.

Let’s scale those mountains, people! and discover the fractal mysteries of the Unknown.

Love, Tonya




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