Friday Fractal XIV

Emergence: Complex patterns arise from the simplest rules. From lighter elements emerge heavier compounds; from clouds of gasses and particles arise galaxies, stars, and planets. From basic atmospheric reactions between basic chemical compounds, the building blocks of life, amino acids emerge. From these acids, patterns of DNA emerge; from DNA, simple life. From simple life forms, complex forms arise, filling countless niches and functions, each form intricately involved from another. From these interactions, ecosystems arise. In these ecosystems, complex beings, dependent upon vast arrays of variables arise. Intelligence emerges, followed by culture, art, symbolism, and technology.

While emergence is everywhere we turn, it seems as if only recently science has begun to look at the concept. Now, Nobel prize winners formally study complexity and emergence. I wouldn't be creating these fractals, themselves emergent structures, unless they had.

Today, I took a Julia set, and applied a kaleidoscopic transformation:

With as complex forms as the formulas allow me to create, I can't even begin to match the emergent beauty in nature, as you see here:

A water lily or "lotus" (Nymphae) blossom emerges from the murky depths of a fish pond.

I find the lotus deeply relevant to some of the ideas I discussed earlier in the week. Living in a world essentially laced with uncertainty, it is sometimes easy to feel like we are helplessly stuck in the mire. With constant change, we struggle to adapt to whatever values we are able to perceive and cling to. It isn't a search for perfection, or beauty. It's pure survival. That's when I try to remember the lotus. It too, struggles to survive. It doesn't seek beauty or perfection. Yet, through that struggle and slime, beauty and perfection emerge, nonetheless.

Of course, I'm certainly not the first to see the lotus as a powerful symbol.

The sacred lotus (Nelumbo nucifera) despite not being native to India, was a cherished symbol of creation to the ancient Hindus. The blossom rising from the mud represented a divine creation. Hindus associated the flower with many deities, including the creator, Brahma, the god of preservation, Vishnu, and the god of potency, Lakshmi.

Early followers of the Buddhist faith later adopted the flower to symbolize divine enlightenment, or nirvana. Like the Hindus, the Buddhists used the lotus extensively in artwork and architectural design. Often, a meditating Buddha statue sat upon a lotus blossom or leaf. Overall, the flower represented a holistic purity; the result cleansing of body, speech, and mind. Different colors of the flower came to represent different aspects, as well as different bodhisattvas (enlightened ones) and meanings. For instance, blue traditionally represents Manjushri, the Bodhisattva of wisdom, while pink, considered the most precious shade, represents Buddha. (For a few more, see ReligionFacts.com.)

The deepest symbolic meanings of the lotus, however, lay not in the color of the flower, but in the process of growth and survival. Rooted in the murky depths of a pond, the lotus blossom emerges from the water, and then opens its petals to the light. Buddha likened this process to the human soul, which wallows in the dark depths of strife before opening to the fresh light and air above. Once enlightened, the soul enjoys the surrounding pristine beauty, while resting atop the turbulent waters of daily life below. "Water surrounds the lotus-flower, but does not wet its petals," Buddha reportedly said in his Sermon at Benares.

The gentle beauty of Buddha's analogies gave central importance to the lotus as a symbol, which is still in wide use today. The lotus has been used as a symbol in meditation, (the lotus position is the most common position in yoga,) become India's national flower, and now graces a line of software, currently owned by IBM. Perhaps the analogy still fits: the lotus emerged from the dark ages into the dazzling modern age.

Painting of Buddha on a blue lotus via Mandalas.com. Lotus photo by the author. All fractals made by the author using ChaosPro.