Tag

Fractals

All articles tagged with #fractals

earth-science15 days ago•13 min saved

The 0.6 Rule: Rivers Shape Fractal Waterways and Deltas

Hack's law: stream length scales roughly as drainage area to the 0.6 power, and it holds worldwide, now extending to river deltas. Through energy-efficient transport networks and landscape-evolution modeling, scientists explain why larger basins elongate rivers, how networks optimize drainage, and why this simple scaling persists even as sediments accumulate at deltas. The work links river bifurcation angles to fivefold symmetry and hints at connections to quasicrystals, revealing a universal geometry of Earth's waterways.

via Quanta Magazine|

#deltas #earth-science #fractals

mathematics1 month ago•22 min saved

Hong Wang Breaks New Ground with 2026 Fields Medal win

Hong Wang and collaborator Joshua Zahl proved the 3D Kakeya set conjecture, a landmark result at the crossroads of harmonic analysis, geometric measure theory, and PDE, earning Wang the 2026 Fields Medal—the third woman to win the prize. The award caps a remarkable journey from Guilin to France, MIT, and NYU, and showcases Wang’s use of multiscale analysis and innovative “sticky” Kakeya techniques to rule out counterexamples, reshaping the field and pointing to future work on higher-dimensional Kakeya problems.

via Quanta Magazine|

#fields-medal #fractals #geometric-measure-theory

science9 months ago•11 min saved

10 Martini' Proof Links Quantum Mechanics to Complex Math Structures

The article discusses the proof of the '10 martini' conjecture, which links quantum mechanics with intricate mathematical structures like fractals and Cantor sets, highlighting the journey from a challenging problem in quantum theory to a breakthrough in understanding energy levels of electrons in magnetic fields, and its implications in physics and mathematics.

via WIRED|

#10-martini-conjecture #fractals #mathematics

science1 year ago•11 min saved

Number Theory Unveils Quantum Fractals in 'Ten Martini' Proof

The article discusses the ten martini conjecture, a challenging problem in quantum physics and mathematics related to the energy levels of electrons in magnetic fields, which was eventually proven using advanced number theory and geometric methods, confirming the fractal patterns known as Hofstadter butterflies as real phenomena.

via Quanta Magazine|

#fractals #hofstadter-butterfly #number-theory

science2 years ago•2 min saved

"The Enigmatic Disruption: How Forests Defy a Fundamental Law of Nature"

A new study from the University of Bristol has found that forest canopies do not replicate the fractal patterns of individual trees, challenging the idea that fractal patterns might explain how forest canopies are organized. The researchers compiled data from nine vastly different forest types in Australia and found that none of the canopy sections behaved like fractals beyond the crowns of individual trees. While forest canopies are not fractal, there is some predictability in how they deviate from fractal patterning, which might still be useful for ecosystem comparisons. The study suggests that forests may prove to be unruly ecosystems that defy mathematical laws, from their canopies right down to their cells.

via ScienceAlert|

#ecology #forest-canopies #fractals

technology3 years ago•3 min saved

Unveiling the Magnetic Secrets of Neuromorphic Computing through Spintronics and X-ray Microscopy

Researchers have made a discovery in the behavior of dynamic magnetic fractal networks, known as skyrmions, which could advance neuromorphic computing capabilities. These skyrmions create magnetic spin waves with a narrow wavelength, forming an unexpected fractal structure. The researchers aim to use this discovery to develop a miniaturized, spin wave neuromorphic architecture. The findings were made through neutron scattering experiments and could have implications for future applications.

via Phys.org|

#fractals #magnetic-materials #neuromorphic-computing