Fractals | L-systems

Fractal canopy

In geometry, a fractal canopy, a type of fractal tree, is one of the easiest-to-create types of fractals. Each canopy is created by splitting a line segment into two smaller segments at the end (symmetric binary tree), and then splitting the two smaller segments as well, and so on, infinitely. Canopies are distinguished by the angle between concurrent adjacent segments and ratio between lengths of successive segments. A fractal canopy must have the following three properties: 1. * The angle between any two neighboring line segments is the same throughout the fractal. 2. * The ratio of lengths of any two consecutive line segments is constant. 3. * Points all the way at the end of the smallest line segments are interconnected, which is to say the entire figure is a connected graph. The pulmonary system used by humans to breathe resembles a fractal canopy, as do trees, blood vessels, viscous fingering, electrical breakdown, and crystals with appropriately adjusted growth velocity from seed. (Wikipedia).

Fractal canopy
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Research: What is a fractal?

Broadcasted live on Twitch -- Watch live at https://www.twitch.tv/leioslabs

From playlist research

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mandelbrot fractal animation 3

red and green.

From playlist Fractal

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Fun with Fractals

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

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mandelbrot fractal animation 4

blue, yellow and green.

From playlist Fractal

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mandelbrot fractal animation 2

just me having my usual fun.

From playlist Fractal

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Coding Math: Episode 40 - Fractal Trees

This time we cover a couple of different ways of creating fractal trees. Even animating them. Support Coding Math: http://patreon.com/codingmath Source Code: http://github.com/bit101/codingmath

From playlist Fractals

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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

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mandelbrot fractal animation 5

another mandelbrot/julia fractal animation/morph.

From playlist Fractal

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Fractal Graph 4

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

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Fractal Christmas Trees

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

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Jörg Thuswaldner: S-adic sequences: a bridge between dynamics, arithmetic, and geometry

Abstract: Based on work done by Morse and Hedlund (1940) it was observed by Arnoux and Rauzy (1991) that the classical continued fraction algorithm provides a surprising link between arithmetic and diophantine properties of an irrational number αα, the rotation by αα on the torus 𝕋=ℝ/ℤT=R/

From playlist Dynamical Systems and Ordinary Differential Equations

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60 years of dynamics and number expansions - 12 December 2018

http://crm.sns.it/event/441/ 60 years of dynamics and number expansions Partially supported by Delft University of Technology, by Utrecht University and the University of Pisa It has been a little over sixty years since A. Renyi published his famous article on the dynamics of number expa

From playlist Centro di Ricerca Matematica Ennio De Giorgi

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S-arithmetic Diophantine approximation - Shreyasi Datta

Special Year Informal Seminar Topic: S-arithmetic Diophantine approximation Speaker: Shreyasi Datta Affiliation: University of Michigan, Ann Arbor Date: December 02, 2022 Diophantine approximation deals with quantitative and qualitative aspects of approximating numbers by rationals. A ma

From playlist Mathematics

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Harmonic measure: Algorithms and applications – Christopher Bishop – ICM2018

Analysis and Operator Algebras Invited Lecture 8.12 Harmonic measure: Algorithms and applications Christopher Bishop Abstract: This is a brief survey of results related to planar harmonic measure, roughly from Makarov’s results of the 1980’s to recent applications involving 4-manifolds,

From playlist Analysis & Operator Algebras

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What is Canopy Clustering | Canopy Clustering in Mahout | Mahout Clustering Tutorial | Edureka

Watch Sample Class Recording: http://www.edureka.co/mahout?utm_source=youtube&utm_medium=referral&utm_campaign=clustering-canopy Canopy Clustering is a very simple, fast and surprisingly accurate method for grouping objects into clusters. All objects are represented as a point in a multi

From playlist Machine Learning with Mahout

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MicroPython Vegetable Garden Automation Tutorial

This MicroPython project adds solar powered sensors and home automation to my vegetable garden and transmits the data using MQTT for review and control on a mobile app. My full write-up for this project: https://www.rototron.info/projects/micropython-vegetable-garden-automation-tutorial/

From playlist ESP32 MicroPython Tutorials

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Simulating Turbulence Over Canopies

By improving our understanding of turbulent flow over canopies we can design better cities to improve air quality. This is just one of the applications of the work of Alfredo Pinelli, a professor at City University of London working on Large Eddy Simulations (LES) of turbulence. Interview

From playlist Fluid Dynamics

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Dimensional Analysis

MIT RES.TLL-004 Concept Vignettes View the complete course: http://ocw.mit.edu/RES-TLL-004F13 Instructor: Ken Kamrin This video leads students through the problem solving method of dimensional analysis. In one example, students use dimensional analysis to determine the diameter of a parac

From playlist MIT STEM Concept Videos

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Nalini Nadkarni: For the Love of Trees | Nat Geo Live

National Geographic grantee and forest ecologist Nalini Nadkarni is known for using nontraditional pathways to raise awareness of nature's importance to human lives, working with artists, preachers, musicians, and even prisoners. ➡ Subscribe: http://bit.ly/NatGeoSubscribe About National G

From playlist National Geographic Live!: Season 6

Related pages

H tree | Graph (discrete mathematics) | Geometry | Fractal | Lichtenberg figure