Vedanta and Fractals: Endlessness Embedded- I Embarked On An Adventurous Meta-Philosophical Journey Translating "Fractal" Into Sanskrit.

Tracing a Concept Through Time and Translation.

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Recently, in an unlikely but fascinating quest, assisted by AI, I had fun thinking about how the word “fractal”, coined by Benoit Mandelbrot in 1975, could have been translated starting from the ancient Indo-European linguistic roots, in particular from the Indo-Iranian branch, and later into Sanskrit. I did this because I strongly believe in the fractal nature of Vedantic teachings and wanted to find parallels at the linguistic level.

The Vedantic notion of Visvatomukham, which means “with the face on all sides”, shares profound resonances with the fractal geometry vision of the universe. Visvatomukham conveys the idea that divine reality shines through all manifested forms. This echoes how fractals reveal self-similar patterns across scales: each microcosm reflects the macrocosm.

The Upanishads proclaim: 

“From fullness comes fullness. When fullness is taken from fullness, Fullness remains”. 

This declares that the infinite ceaselessly pours from the eternal source, which is never depleted. Mathematically too, fractals iterate infinitely to generate immense complexity from simplicity. The fundamental pattern is preserved within each iteration.

In Vedanta, Brahman is understood as the fundamental reality transcending and expressing the diversified universe. Fractals symbolize this interplay between unity and diversity, the interpenetration of the whole within each part. They represent the wondrous interdependence between part and whole.