A type of chaos found in everything from prime numbers to turbulence can unify a pair of unrelated ideas, revealing a ...

A new study reveals that Srinivasa Ramanujan’s century-old formulas for calculating pi unexpectedly emerge within modern theories of critical phenomena, turbulence, and black holes. In school, many of ...

Creative Commons (CC): This is a Creative Commons license. Attribution (BY): Credit must be given to the creator. This paper introduces fractal analysis to study the kinetics of biomass hydrothermal ...

The Nature Index 2025 Research Leaders — previously known as Annual Tables — reveal the leading institutions and countries/territories in the natural and health sciences, according to their output in ...

You may not be able to define “fractal” — yet — but fractals are, in fact, everywhere. As you might expect from hearing her title, Hayley Brazier, Donald M. Kerr curator of natural history at the High ...

Abstract: In this paper, the discrete complex-valued dynamics is used to solve nonlinear equations to generate fractals. This new class of fractals, called Zhang fractals, are different from the ...

@brief This struct represents a complex number. @var a Represents the real part of the complex number. @var b Represents the imaginary part of the complex number. @brief This struct holds most of the ...

x2=sqrt(beta*(r-1)); y2=sqrt(beta*(r-1)); z2=r-1; x3=-sqrt(beta*(r-1)); y3=-sqrt(beta*(r-1)); z3=r-1; ...

Abstract: This article discusses the construction of fractal equations, the classical set of Cantor and consisting of spirals based on theories of R-functions (RFM), using recursion procedures.