Types of functions | Fractal curves
A fractal curve is, loosely, a mathematical curve whose shape retains the same general pattern of irregularity, regardless of how high it is magnified, that is, its graph takes the form of a fractal. In general, fractal curves are nowhere rectifiable curves — that is, they do not have finite length — and every subarc longer than a single point has infinite length. A famous example is the boundary of the Mandelbrot set. (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
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From playlist research
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
Sierpinski's triangle as a fractal curve
From playlist Space filling curves
mandelbrot fractal animation 5
another mandelbrot/julia fractal animation/morph.
From playlist Fractal
Summer of math exposition submission- fractal calculus
Fractal Calculus
From playlist Summer of Math Exposition Youtube Videos
The Beauty of Fractal Geometry (#SoME2)
0:00 — Sierpiński carpet 0:18 — Pythagoras tree 0:37 — Pythagoras tree 2 0:50 — Unnamed fractal circles 1:12 — Dragon Curve 1:30 — Barnsley fern 1:44 — Question for you! 2:05 — Koch snowflake 2:26 — Sierpiński triangle 2:47 — Cantor set 3:03 — Hilbert curve 3:22 — Unnamed fractal squares 3
From playlist Summer of Math Exposition 2 videos
!!Con West 2019 - Michael Malis: Generating fractals … with SQL queries!!!
Presented at !!Con West 2019: http://bangbangcon.com/west SQL databases can do a lot. They are fantastic at making it easy to work with large amounts of data. One of the lesser-known capabilities of SQL databases is that they can be used to generate fractals! In this talk, we’ll take a l
From playlist !!Con West 2019
Ahlfors-Bers 2014 "Conformal invariance and critical behavior within critical fractal carpets"
Wendelin Werner (ETH Zürich): Some aspects of conformal invariance can survive within fractal carpets in the plane. In the present talk, I will survey how it is possible to make sense in a rather precise way of certain of these ideas in the special case of certain random -- yet very natura
From playlist The Ahlfors-Bers Colloquium 2014 at Yale
!!Con West 2019 - Michael Malis: Generating fractals … with SQL queries!!!
Presented at !!Con West 2019: http://bangbangcon.com/west SQL databases can do a lot. They are fantastic at making it easy to work with large amounts of data. One of the lesser-known capabilities of SQL databases is that they can be used to generate fractals! In this talk, we’ll take a l
From playlist !!Con West 2019
Coding Math: Episode 35 - Intro to Fractals
Here, we begin with one of my favorite mathematical subjects, fractals. This won't be a long fractal marathon, but I'll be dropping a fractal episode now and again. Check out my book on creating fractals with JavaScript, "Playing With Chaos" http://www.playingwithchaos.net Support Codin
From playlist Fractals
Mandelbulbs: the search for a 3D Mandelbrot Fractal
Follow Tom on his journey to Delft in the Netherlands in his quest to find a 3D Mandelbrot Set, otherwise known as a 'Mandelbulb'. We begin with a discussion of the definition of a fractal, with examples from the natural world, as well as generating our very own in the form of the Koch Sn
From playlist Director's Cut
Douglas McKenna - Half-Domino Curves in an Interactive Math Book - G4G14 Apr 2022
The well-known Hilbert Curve, with its non-fractal square boundary, turns out to be a special case of a larger class of space-filling curves of unit area called "half-domino" curves. These are also tiles in the limit, but with infinitely long, almost-everywhere linear boundaries that are b
From playlist G4G14 Videos
8.3: Fractal Recursion with ArrayList of Objects (Koch Curve) - The Nature of Code
This video looks at how to use an ArrayList to store the parts of a fractal as separate objects. This allows a fractal to experience physics. The Koch curve is used as a demonstration. (If I reference a link or project and it's not included in this description, please let me know!) Rea
From playlist The Nature of Code: Simulating Natural Systems
Newton’s method, and the fractal it creates that Newton knew nothing about
Who knew root-finding could be so complicated? Next part: https://youtu.be/LqbZpur38nw Special thanks to the following supporters: https://3b1b.co/lessons/newtons-fractal#thanks An equally valuable form of support is to simply share the videos. ------------------ Interactive for this vid
From playlist Explainers
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 is an infinite zoom on the famous Sierpinski triangle fractal. If you want to see six different constructions of this fractal, check out this long form video I made : https://youtu.be/IZHiBJGcrqI . #math #manim #fractal #sierpinski #zoom #infinite #shorts #mathshorts
From playlist Fractals