3Blue1Brown
Fractals are typically not self-similar
What exactly are fractals? A common misconception is that they are shapes which look exactly like themselves when you zoom in. In fact, the definition has something to do with the idea of "fractal dimension".
3Blue1Brown
Hilbert's Curve: Is infinite math useful?
Drawing curves that fill all of space, and a philosophical take on why mathematics about infinite objects can still be useful in finite contexts.
SciShow
How a Butterfly’s Wingbeat CAN Change the Weather
You may have heard of the butterfly effect, where butterflies flapping their wings somehow cause tornadoes. Although it seems pretty unlikely, butterflies can affect the weather, just not in the way you might think.
3Blue1Brown
Where Newton meets Mandelbrot (Holomorphic dynamics)
How the right question about Newton's method results in a Mandelbrot set.
Curated Video
Fractals: The Koch Snowflake
The characteristics of Koch's mathematical fractal are produced by following a set of simple rules, which result in an infinitely reducing pattern. Maths - Shape A Twig Math Film. Reinforce and extend the learning required by the...
PBS
Human Tree: Dilations
Look at dilations exponentially. Using a fractal from a museum exhibit, the installment from the Math at the Core: Ratios series introduces the term dilation. The presenter points out that dilations can make images either smaller or...
PBS
Human Tree: Ratios
Create a personal tree. By visiting an exhibit at the National Museum of Mathematics, the resource introduces the idea of fractals. The exhibit takes an image of the person and creates a tree by repeating scaled images on the shoulders...
CK-12 Foundation
Self Similarity: Lesson
Zoom in to reveal more of the same. The resource introduces the concept of self similarity. Using a simple example, the video—part of a larger playlist covering geometry concepts—illustrates the meaning of a self similarity figure.
Numberphile
Pi and the Mandelbrot Set
Pi shows up in a lot of places, even in the complex plane. Individuals watch a video in the Numberphile Pi series that shows the Mandelbrot set in the complex plane and explains how pi shows up in the number of iterations.
Veritasium
What Is The Coastline Paradox?
Measurements of Australia's coast line range from 12,500 km long to 25,700 km long. What causes the difference in these measurements? The video discusses the coastline paradox, fractals, and the importance of the size of a measuring stick.
TED-Ed
Fractals and the Art of Roughness
Roughness is everywhere, contributing to the incredible complexity of the world around us. This complexity, however, is not without it's own unique sense of order. Join world-renown mathematician Benoit Mandelbrot as he looks...
3Blue1Brown
Fractal Charm: Space Filling Curves
Viewers fill their minds with space-filling curves watching a video of animations that show examples of space-filling curves, such as the Peano curve and the "Flow Snake" curve. The video also illustrates how space-filling curves...
Massachusetts Institute of Technology
Mit: Blossoms: Fabulous Fractals and Difference Equations
Former MIT student introduces the classroom to fractal geometry via a video presentation appropriate for students who have had two years of high school algebra. Video lesson content includes the "chaos game" and trajectory calculations...
Massachusetts Institute of Technology
Mit: Blossoms: Fabulous Fractals and Difference Equations
This learning video introduces students to the world of Fractal Geometry through the use of difference equations. [32:31]
Other
Mitk12: What Is a Fractal (And What Are They Good For)?
Fractals are complex, never-ending patterns created by repeating mathematical equations. Yuliya, an undergrad in Math at MIT, delves into their mysterious properties and how they can be found in technology and nature. [4:12]
Khan Academy
Khan Academy: Geometry: Area of Koch Snowflake (Part 1) Advanced
Demonstrates how to find the area of a Koch snowflake by summing an infinite geometric series based on the area of an equilateral triangle. [12:30]
Khan Academy
Khan Academy: Geometry: Koch Snowflake Fractal
Explanation of the Koch Snowflake and why it has an infinite perimeter but a finite area. [9:11]
Khan Academy
Khan Academy: Geometry: Area of Koch Snowflake (Part 2) Advanced
Explains how to find the area of a Koch snowflake which is represented by an infinite geometric series. Continuation of previous video "Area of Koch Snowflake (part 1) - Advanced" [6:32]
Massachusetts Institute of Technology
Mit: Science Out Loud: What Is a Fractal?
Fractals are complex, never-ending patterns created by repeating mathematical equations. Yuliya, an undergrad in Math at MIT, delves into their mysterious properties and how they can be found in technology and nature. [4:12]
Khan Academy
Khan Academy: Triangles: Koch Snowflake Fractal
Explanation of the Koch Snowflake and why it has an infinite perimeter but a finite area.
Khan Academy
Khan Academy: Vi Hart: Fractal Fractions
Video exploring equivalent fractions and how fractions can be written in a fractal or binary tree structure. Solving algebraic equations and infinite convergence mentioned. [5:45]
Khan Academy
Khan Academy: Vi Hart: Doodling in Math: Infinity Elephants
Video demonstrating some drawing games that illustrate mathematical concepts of series and infinite series such as fractals and the Sierpinski triangle. [4:36]
Khan Academy
Khan Academy: Doodling in Math: Doodling in Math: Infinity Elephants
Video demonstrating some drawing games that illustrate mathematical concepts of series and infinite series such as fractals and the Sierpinski triangle.
Khan Academy
Khan Academy: Vi Hart: Doodling in Math: Binary Trees
Video demonstrating how to draw binary trees and exploring some of the interesting shapes and patterns that can be made from them. [3:48]