Fractal geometry of critical systems

A study on dimensions of Fractal geometry in Iranian architecture

The subject of geometry and proportions has been regarded as an issue which has a close relationship with architecture. Since the entire universe, living beings and the human geometry can be seen clearly, that’s why our unconscious essence has accustomed to these proportions whereby reflection of this mentality can be seen in the architect’s hands and thought in the architecture. It can witness...

Manufacturability of Fractal Geometry

Nowadays more and more aesthetic product developments, assemblage and decoration designs are taking aesthetically appealing forms of natural objects such as rough terrain, ripples on lakes, coastline and seafloor topography. They are mathematical definable via fractal geometry theory and emerge to attract a lot of attention. However, not many methods for manufacturing of fractal objects have be...

EcoGenomics: analysis of complex systems via fractal geometry.

Ecogenomics is a convenient descriptor for the application of advanced molecular technologies to studies of organismal responses to environmental challenges in their natural settings. The development of molecular tools to survey changes in the transcript profile of thousands of genes has presented scientists with enormous analytical challenges. In the main, these center about the reduction of m...

Extending the Geometry to Systems of Fractal Cities

Percolation fractal exponents without fractal geometry

Classically, percolation critical exponents are linked to the power laws that characterize percolation cluster fractal properties. It is found here that the gradient percolation power laws are conserved even for extreme gradient values for which the frontier of the infinite cluster is no more fractal. In particular the exponent 7/4 which was recently demonstrated to be the exact value for the d...