A fractal is an irregular geometric object with an infinite nesting of structure at all scales. It is mainly applicable in soil chromatography and soil micromorphology (Anderson, 1997). Internal structure, pore size distribution and pore geometry can be identified by using fractal dimension at nano scale. As soil is heterogeneous the pore spaces are made up of macropores, micropores and mesopores. When soil is studied in nanoscale it the macropore are composed of micro and meso pore and further they are composed of organo-mineral complex. The fractal approach to soil mechanics is a new line of thought. It was first raised in "Fractal Character Of Grain-Size Distribution Of Expansion Soils" by Yongfu Xu and Songyu Liu, published in 1999, by Fractals. There are several problems in soil mechanics which can be dealt by applying a fractal approach. One of these problems is the determination of soil-water-characteristic curve (also called (water retention curve) and/or capillary pressure curve). It is a time-consuming process considering usual laboratory experiments. Many scientists have been involved in making mathematical models of soil-water-characteristic curve (SWCC) in which constants are related to the fractal dimension of pore size distribution or particle size distribution of the soil. After the great mathematician Benoît Mandelbrot—father of fractal mathematics—showed the world fractals, Scientists of Agronomy, Agricultural engineering and Earth Scientists have developed more fractal-based models. All of these models have been used to extract hydraulic properties of soils and the potential capabilities of fractal mathematics to investigate mechanical properties of soils. Therefore, it is really important to use such physically based models to promote our understanding of the mechanics of the soils. It can be of great help for researchers in the area of unsaturated soil mechanics. Mechanical parameters can also be driven from such models and of course it needs further works and researches. is a framework that includes functions with fractal support. Anderson, A.N., McBratney, A.B. and Crawford, J.W., 1997. Applications of fractals to soil studies. In Advances in Agronomy (Vol. 63, pp. 1-76). Academic Press. * v * t * e * v * t * e (Wikipedia).
Fractals are typically not self-similar
An explanation of fractal dimension. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/fractals-thanks And by Affirm: https://www.affirm.com/careers H
From playlist Explainers
In this video, I define a neat concept called the fractal derivative (which shouldn't be confused with fractional derivatives). Then I provide a couple of examples, and finally I present an application of this concept to the study of anomalous diffusion in physics. Enjoy!
From playlist Calculus
Broadcasted live on Twitch -- Watch live at https://www.twitch.tv/leioslabs
From playlist research
Summer of math exposition submission- fractal calculus
Fractal Calculus
From playlist Summer of Math Exposition Youtube Videos
mandelbrot fractal animation 5
another mandelbrot/julia fractal animation/morph.
From playlist Fractal
What are fractals? Just look at your broccoli to find out! License: Creative Commons BY-NC-SA More information at http://k12videos.mit.edu/terms-conditions
From playlist Measurement
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/8wEX
From playlist 3D printing
If Aliens Invaded Earth | Alien Encounters (Full Episode)
The Arrival has ended. A swarm of small spacecraft depart their huge mothership, and hover in our atmosphere. The ships open their hatches, and deposit thousands of mysterious pods on the earth's surface. Are they a message, a gift or a weapon? Stream More Episodes of Alien Encounters: ht
From playlist Full Episodes: Alien Encounters
Rate-Induced Tipping in Asymptotically Autonomous Dynamical Systems: Theory.. by Sebastian Wieczorek
PROGRAM TIPPING POINTS IN COMPLEX SYSTEMS (HYBRID) ORGANIZERS: Partha Sharathi Dutta (IIT Ropar, India), Vishwesha Guttal (IISc, India), Mohit Kumar Jolly (IISc, India) and Sudipta Kumar Sinha (IIT Ropar, India) DATE: 19 September 2022 to 30 September 2022 VENUE: Ramanujan Lecture Hall an
From playlist TIPPING POINTS IN COMPLEX SYSTEMS (HYBRID, 2022)
The Newton Fractal Explained | Deep Dive Maths
A Newton fractal is obtained by iterating Newton's method to find the roots of a complex function. The iconic picture of this fractal is what I call The Newton Fractal, and is generated from the function f(z)=z^3-1, whose roots are the three cube roots of unity. What is the history of th
From playlist Deep Dive Maths
Umberto Mosco - 21 September 2016
Mosco , Umberto "Beyond perimeters, between discrete and continuous structures"
From playlist A Mathematical Tribute to Ennio De Giorgi
Working on the Fractal Flame method for creating some Christmas trees! I'm hoping it works out before Christmas! -- Watch live at https://www.twitch.tv/simuleios
From playlist Misc
Tipping in Thermoacoustic Systems and Their Early Warning Signals by R. I. Sujith
PROGRAM TIPPING POINTS IN COMPLEX SYSTEMS (HYBRID) ORGANIZERS: Partha Sharathi Dutta (IIT Ropar, India), Vishwesha Guttal (IISc, India), Mohit Kumar Jolly (IISc, India) and Sudipta Kumar Sinha (IIT Ropar, India) DATE: 19 September 2022 to 30 September 2022 VENUE: Ramanujan Lecture Hall an
From playlist TIPPING POINTS IN COMPLEX SYSTEMS (HYBRID, 2022)
Delicia Kamins - Philosophy of Fractals - CoM Oct 2020
We know that fractals are nature’s pattern makers. Fractals are in fact everywhere we look: tree bark, snowflakes, mountain ranges, cloud, rivers, seashells, all the way up to the shape of galaxies. Beyond nature, however, human beings are fractal thinkers. We depend on fractal algorithms
From playlist Celebration of Mind
Integrability in the Laplacian Growth Problem by Eldad Bettelheim
Program : Integrable systems in Mathematics, Condensed Matter and Statistical Physics ORGANIZERS : Alexander Abanov, Rukmini Dey, Fabian Essler, Manas Kulkarni, Joel Moore, Vishal Vasan and Paul Wiegmann DATE & TIME : 16 July 2018 to 10 August 2018 VENUE : Ramanujan L
From playlist Integrable systems in Mathematics, Condensed Matter and Statistical Physics
Tim Palmer on Doubt: From Quantum Physics to Climate Change | Closer To Truth Chats
Tim Palmer discusses his new book, The Primacy of Doubt: From Quantum Physics to Climate Change, How the Science of Uncertainty Can Help Us Understand Our Chaotic World. In it, he challenges conventional wisdom on quantum mechanics, free will, and more. Order The Primacy of Doubt: https:/
From playlist Closer To Truth Chats
An invitation to nonlocal modeling, analysis and computation – Qiang Du – ICM2018
Numerical Analysis and Scientific Computing | Mathematics in Science and Technology Invited Lecture 15.2 | 17.2 An invitation to nonlocal modeling, analysis and computation Qiang Du Abstract: This lecture serves as an invitation to further studies on nonlocal models, their mathematics, c
From playlist Numerical Analysis and Scientific Computing