Chaos Game Exploration of Triple Vertex Polygons John Paul, Thomas, Bjorn GUTS/Challenge STI 2009.

Slides:

Advertisements

Similar presentations

Fractals with a Special Look at Sierpinskis Triangle By Carolyn Costello.

Advertisements

40S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Sequences Lesson: SEQ-L3 Drawing Fractal Patterns Drawing Fractal Patterns Learning Outcome.

More About Recursion - 2 Java. Looking at more recursion in Java A simple math example Fractals.

Math Modeling Final Project APPLICATIONS of FRACTALS Advisor: Professor Alber Fang Qi Pu Wan Xue Rui FRACTAL LANDSCAPES FRACTAL IMAGE COMPRESSION.

FIELD DAY TOK: Mathematics and Imagination

West Wallsend High School Visit September 24 th 2010 West Wallsend High School Visit Presentation by Jon Borwein, Director Centre for Computer Assisted.

Linear Fractal Mountains 2 step recursive process: –Subdivide chain by creating edge midpoints –Randomly perturb midpoint positions Gen 0: Gen 1: Gen 2:

The Wonderful World of Fractals

Geometry Surface Area of Pyramids and Cones

Gattegno Tens Charts Term 1 Mathematics.

Iterated Function Systems (IFS) and Fractals Math 204 Linear Algebra November 16, 2007.

Applied Mathematics Complex Systems Fractals Fractal by Zhixuan Li.

A PowerPoint presentation brought to you by Christian Malone and Alissa Ousley.

HONR 300/CMSC 491 Computation, Complexity, and Emergence Mandelbrot & Julia Sets Prof. Marie desJardins February 22, 2012 Based on slides prepared by Nathaniel.

FRACTALS OF THE WORLD By Leslie Ryan. Common Terms Iteration- To repeat a pattern multiple times, usually with a series of steps. Reflection- An image.

Surface Area of Pyramids and Cones Section 12.3 Goal – to find the surface area of a pyramid and the surface area of a cone.

Geometry 11-3 Surface Areas of Pyramids and Cones.

Similar Triangles and Polygons

Fractal Composition of Meaning: Toward a Collage Theorem for Language Simon D. Levy Department of Computer Science Washington and Lee University Lexington,

Structured Chaos: Using Mata and Stata to Draw Fractals

An Introduction to Fractals By: Brian Feuer What is a Fractal? A word coined by Benoit Mandelbrot in 1975 to describe shapes that are “self-similar”

How complex ~ Developed by Andrew Derer ~ MathScience Innovation Center, Richmond, VA.

The Chaos Game.

CATCH SCRATCH! Programming from Scratch. Remember Scratch?

Vertex – A point at which two or more edges meet Edge – A line segment at which two faces intersect Face – A flat surface Vertices, Edges, Faces.

Catch the Spirit of Mathematical Practices Mathematics Investigations Chaos Game Rules:  Starting point is any point in the plane of triangle ABC.  Second.

SPSU, Fall 08, CS6353 Alice In Wonderland! Richard Gharaat.

Elementary Linear Algebra Howard Anton Copyright © 2010 by John Wiley & Sons, Inc. All rights reserved. Chapter 10.

Fractals Douglas reeves.

Warm Up 3. Directions: Use this set of digits to write and equation that will be as close to 100 as possible. Explain why this is as close to 100 as you.

Copyright © Curt Hill Visualization of 3D Worlds How are these images described?

David Chan TCM and what can you do with it in class?

Chapter Surface Area of Pyramids and Cones.

Section 6.1 Images Viewing a Gallery of Fractals. Look for patterns.

TESSELLATIONS A Tessellation (or Tiling) is a repeating pattern of figures that covers a plane without any gaps or overlaps.

Fractals! Fractals are these crazy objects which stretch our understanding of shape and space, moving into the weird world of infinity. We will look at.

09/02/2016 Celtic Knot Patterns 3 Maths Today we will explore and mathematically describe border patterns. Big Idea: Maths and Graphic Design.

Warm Up Jordan multiplied 20 x 500 and provided his answer as 10,000. Mike told him that he was incorrect. He said that since the problem only had three.

THE MAPLE LEAF FRACTAL Christina VoEPS 109 Fall 2013.

Insert Lesson Title Here Course Volume of Pyramids and Cones A pyramid is a three-dimensional figure whose base is a polygon, and all of the other.

Creating a Hat Curve Fractal Objectives: 1.To create a Hat Curve fractal on Geometer’s Sketchpad using iteration. 2.To find the length of the Hat Curve.

A Primer on Chaos and Fractals Bruce Kessler Western Kentucky University as a prelude to Arcadia at Lipscomb University.

Spencer Hart Advisor: Gus Hart

The point opposite the base of the pyramid

HONR 300/CMSC 491 Computation, Complexity, and Emergence

Warm Up Evaluate. 1. (-1)8 2. (11)2 3. (–9)3 4. (3)4

UKS2 Topic: Early Islamic Civilisation

Fractals Project Natalie Rowe.

HONR 300/CMSC 491 Fractals (Flake, Ch. 5)

FUN With Fractals and Chaos!

HONR 300/CMSC 491 Fractals (Flake, Ch. 5)

Given the series: {image} and {image}

You need: Pencil Agenda Scrap Paper AP log Math book Calculator

Fun with Sierpinski Pyramids

S.K.H. Bishop Mok Sau Tseng Secondary School

HONR 300/CMSC 491 Fractals (Flake, Ch. 5)

The Wonderful World of Fractals

Surface Area of Pyramids and Cones

Both series are divergent. A is divergent, B is convergent.

Spire Math Examples of Games with Short Cuts

Modeling the Ikeda Map By: Jonathan Eads

Click the box to reveal the coin

Surface Area and Volume

Gattegno Tens Charts Term 1 Mathematics.

$25,000 Pyramid Game.

Hazelwood School District

Which sequence is linear? How do you know?

Writing Rules for Linear Functions Pages

Presentation transcript:

Chaos Game Exploration of Triple Vertex Polygons John Paul, Thomas, Bjorn GUTS/Challenge STI 2009

Chaos Game Method of describing a fractal pattern OR attractor of an iterated function set. Agents hop around randomly on the surface, instead of traditional methods of testing to see whether each iterated function is a part of the fractal (i.e. cutting). Coined by Michael Barnsley.

The Math Starting with any point x 0, successive iterations are formed as x k+1 = f r (x k ). Where f r is a member of the given IFS randomly selected for each iteration. The iterations converge to the fixed point of the iterated function series. Whenever x 0 belongs to the attractor of the IFS, all iterations x k stay inside the attractor and.

The Model Start with original Serpinski Chaos Game code (written by Nick Bennett) What happens when we vary the factor? I.E. Instead of ½, how about.23 or.75?

Results

Results Contd

Expanding the Model/Project Pull the mathematics out of the equation: Jonathan Wolfe, HELP ME!

References Wikipedia! Bennett, N. NetLogo Mystery Model.