Fractal Markeets

Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary.

Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary.

This book includes chapters that discuss applications and updates in fractal analysis across the full spectrum of sciences, including mathematical concepts, cities, material physics, medicine, climate, and image processing.

The aim of this book is to show some applications of fractal analysis in the fields of sciences.

Ultra Fractal is the best tool to create fractal art. It is very easy to use and yet more powerful than any other fractal program.Get started quickly with the integrated tutorialsIt is easy and fun to start using Ultra Fractal with the built-in tutorials. Starting with the basics, you will soon learn how to create your own fractals, change the colors, add layers, use masks, and even create animations. You can also download the PDF manual to print the tutorials.

Ultra Fractal is the best tool to create fractal art. It is very easy to use and yet more powerful than any other fractal program.Get started quickly with the integrated tutorialsIt is easy and fun to start using Ultra Fractal with the built-in tutorials. Starting with the basics, you will soon learn how to create your own fractals, change the colors, add layers, use masks, and even create animations. You can also download the PDF manual to print the tutorials.

This volume is dedicated to Fractal geometry. The reader will be introduced to the most recent results in these subjects. Researchers and graduate students alike will benefit from the clear expositions.