Iterated function system fractals

Iterated function system

In mathematics, iterated function systems (IFSs) are a method of constructing fractals; the resulting fractals are often self-similar. IFS fractals are more related to set theory than fractal geometry. They were introduced in 1981. IFS fractals, as they are normally called, can be of any number of dimensions, but are commonly computed and drawn in 2D. The fractal is made up of the union of several copies of itself, each copy being transformed by a function (hence "function system"). The canonical example is the Sierpiński triangle. The functions are normally contractive, which means they bring points closer together and make shapes smaller. Hence, the shape of an IFS fractal is made up of several possibly-overlapping smaller copies of itself, each of which is also made up of copies of itself, ad infinitum. This is the source of its self-similar fractal nature. (Wikipedia).

Iterated function system
Video thumbnail

Comparing Iterative and Recursive Factorial Functions

Comparing iterative and recursive factorial functions

From playlist Computer Science

Video thumbnail

Functions of equations - IS IT A FUNCTION

👉 Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r

From playlist What is the Domain and Range of the Function

Video thumbnail

Determine if a Relation is a Function

http://mathispower4u.wordpress.com/

From playlist Intro to Functions

Video thumbnail

Definition of an Injective Function and Sample Proof

We define what it means for a function to be injective and do a simple proof where we show a specific function is injective. Injective functions are also called one-to-one functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear https://amzn.to/3BFvcxp (these are my affil

From playlist Injective, Surjective, and Bijective Functions

Video thumbnail

What is a function?

This video explains what a mathematical function is and how it defines a relationship between two sets, the domain and the range. It also introduces three important categories of function: injective, surjective and bijective.

From playlist Foundational Math

Video thumbnail

Using the vertical line test to determine if a graph is a function or not

👉 Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r

From playlist What is the Domain and Range of the Function

Video thumbnail

Definition of a Surjective Function and a Function that is NOT Surjective

We define what it means for a function to be surjective and explain the intuition behind the definition. We then do an example where we show a function is not surjective. Surjective functions are also called onto functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear ht

From playlist Injective, Surjective, and Bijective Functions

Video thumbnail

Determine if the equation represents a function

👉 Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r

From playlist What is the Domain and Range of the Function

Video thumbnail

.999...=1 and Fractal Geometry | Nathan Dalaklis

A bit of Algebra is the quickest way to see that .9 repeating equals 1, but there is another approach from the lens of fractal geometry using iterated functions systems (IFSs). These mathematical devices are used to created different fractals, but they can also be used to fundamentally des

From playlist The New CHALKboard

Video thumbnail

Iterators: The Next Iteration

Iterators are a generalization of lists that are accessed one element at a time. Iterators allow us to work with data whose length is infinite or unknown, and they avoid the explicit generation of all elements at the same time, by using incremental generators. First presented a year ago, t

From playlist Wolfram Technology Conference 2022

Video thumbnail

Mohammad Farazmand: "Accelerated Gradient Optimization: A Multiscale Analysis"

Machine Learning for Physics and the Physics of Learning 2019 Workshop III: Validation and Guarantees in Learning Physical Models: from Patterns to Governing Equations to Laws of Nature "Accelerated Gradient Optimization: A Multiscale Analysis" Mohammad Farazmand - North Carolina State Un

From playlist Machine Learning for Physics and the Physics of Learning 2019

Video thumbnail

Jorge Nocedal: "Tutorial on Optimization Methods for Machine Learning, Pt. 1"

Graduate Summer School 2012: Deep Learning, Feature Learning "Tutorial on Optimization Methods for Machine Learning, Pt. 1" Jorge Nocedal, Northwestern University Institute for Pure and Applied Mathematics, UCLA July 19, 2012 For more information: https://www.ipam.ucla.edu/programs/summ

From playlist GSS2012: Deep Learning, Feature Learning

Video thumbnail

7. Solutions of Nonlinear Equations; Newton-Raphson Method

MIT 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2015 View the complete course: http://ocw.mit.edu/10-34F15 Instructor: James Swan This lecture talked about the system of non-linear equations. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/term

From playlist MIT 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2015

Video thumbnail

Am I attracted to the Sierpinski triangle?

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

From playlist research

Video thumbnail

Stanford CS229: Machine Learning | Summer 2019 | Lecture 15 - Reinforcement Learning - II

For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3E8Do7X Anand Avati Computer Science, PhD To follow along with the course schedule and syllabus, visit: http://cs229.stanford.edu/syllabus-summer2019.html

From playlist Stanford CS229: Machine Learning Course | Summer 2019 (Anand Avati)

Video thumbnail

An Apple a Day Can Solve World Hunger (Chaos Theory: Butterfly Effect) #SoME2

Thanks to RJTheLammie and an anonymous maths teacher for helping with this project. They both contributed massively, so they deserve as much, if not more credit for this video. This was an absolute pain to create. 20 minutes of coded simulations, Manim animations, suffering, video editing

From playlist Summer of Math Exposition 2 videos

Video thumbnail

The design of functional numerical software - Dr Richard Mortier, University of Cambridge

Owl is an OCaml library for engineering and scientific computing. The library is developed in the functional language and possesses many unique designs in its architecture. The goal is to allow programmers to write code as concise as Python yet as fast as C with advanced features inherited

From playlist Turing Seminars

Video thumbnail

Introduction to Relations and Functions (L9.1)

This lesson introduces functions and explains how to determine if a relations is a function. The vertical line also used. Video content created by Jenifer Bohart, William Meacham, Judy Sutor, and Donna Guhse from SCC (CC-BY 4.0)

From playlist Introduction to Functions: Function Basics

Video thumbnail

How to determine if an ordered pair is a function or not

👉 Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r

From playlist What is the Domain and Range of the Function

Video thumbnail

Allesandro Lazaric: Reinforcement learning - lecture 2

CIRM HYBRID EVENT Recorded during the meeting "Mathematics, Signal Processing and Learning" the January 28, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians o

From playlist Virtual Conference

Related pages

Hutchinson operator | Set theory | Closure (topology) | Inverse problem | Sierpiński triangle | Collage theorem | Monoid | Ad infinitum | Iterated function | Mathematics | Affine transformation | Fractal flame | Fractal compression | L-system | Möbius transformation | Compact space | De Rham curve | Contraction mapping | Function composition | Infinite compositions of analytic functions | Fractal | Matrix (mathematics) | Complete metric space | Binary tree | Cantor set | Projective transformation | Chaos game | Complex-base system