Duality of Zed #646/665
This artwork explores patterns not merely described by or created by mathematics, but rather pre-existing structures uncovered through mathematical relationships. These are forms that emerge naturally from pure logic through concise yet powerful expressions like ln(-z)/ln(z) or ln(z)/(z+1). Using computers as microscopes, viewers can explore these patterns across a zoom range spanning more than 25 orders of magnitude, from macroscopic scales down to microscopic depths, where individual pixels represent regions smaller than subatomic particles. While each piece is distinct, they're all unified by overarching families of equations, related like neighboring species.
Through years of exploration, most of the rules and variations I tried failed to produce any images with interesting features. Countless boring blobs and torn unaesthetic plots were rendered amidst a sea of static and emptiness as I searched for anything worth further exploration. But on the rarest occasions, something exciting would happen (!) -- a doorway to something alien and infinitely explorable would suddenly materialize in my viewport, and this excitement would encourage me to keep looking for the next. I've gathered my favorite discoveries into a curated set, intentionally leaving room across hundreds of attributes for collectors to evolve the collection according to their own curiosity. With equations centered vertically, a sense of pareidolia invites viewers to find their own meanings, as personalized structures emerge simultaneously strange yet familiar, unique for each observer. What do you see?
Over 100 color palettes are available, each with unique color orderings and shading parameters passed down their lineages. Complexity increases along a depth curve the more it is evolved by collectors.
Random:
- Border, Orientation
Root Depth:
- Palette, Magic Numbers
Depth 1:
- Orbit, Blending
Depth 5:
- Equation
Depth Cycle:
- Formula
Press the S key to save an HD render. Use P to export a UHD print.
