PPT-Fractals

Part 1 In which we attempt to describe what a fractal is because people will ask but perhaps they will not really want to know the answer Then I introduce the 2 nd most photogenic fractal of the class and attempt to convince you it is cool anyways. andelbrot The ractal Geometry of ature reeman ew York 1177 fractals have experienced considerable success in quantifying the complex structure exhibited by many natural patterns and have capturedtheimaginationsofscientistsandartistsalikeWithever4wide Functional Programming Composing Fractals MARK P JONES Department of Computer Science Engineering OGI School of Science Engineering at OHSU 20000 NW Walker Road Beaverton OR 97006 USA Abstract This paper describes a simple but 64258exible famil thisnotionmorethoroughlyinSection1.3.Notonlyaredoublingmetricsinterestingobjectsintheirownright,buttheyarealsoofpracticalconcern.Growthrestrictionsareverynaturalandarethoughttooccurinreal-worldphenome St Paul’s Geometry Masterclass II. Who are we?. Mairi Walker. Final year maths PhD student at The Open University. Studying links between geometry and numbers. A. lso interested in the history of maths. Using Mata and . Stata. . to Draw Fractals. Seth Lirette, MS. Inspiration. Types . Of. Fractals. Escape-time. . Fractals. Formula iteration in the complex plane. Iterate many times. If doesn’t diverge to infinity, it belongs in the set and you mark it.. Arcadia is actually a regional district in Greece, which is located on the Peloponnesian peninsula. In Greek mythology, it was the home of Pan, the god of pastoralism and hunting. He was known for seducing goddesses and nymphs. He wandered the hills and mountains of Arcadia, chasing after such nymphs. Arcadia was meant to be a form of paradise, one that all supernatural creatures inhabited (and not one for the deceased).. Play the Chaos Game . Learn to Create . Your Own Fractals. Jumping Seeds. Start: . Choose a corner of the triangle. This is your . first seed. .. Jump:. . Choose . a . corner . (that is not your seed). . : NEW PARADIGMS IN LINEAR WAVE PHYSICS Maria Mylova , James M. Christian, and Graham S. McDonald m.mylova @edu.salford.ac.uk & j.christian @salford.ac.uk Materials & Physics Research Centre , Universi Geoengineering. . by . Injection . of . Solid Particles. : . Risks . and . Benefits. . Preliminary Assessment of . Al. 2. O. 3. . Geoengineering. :. Microphysics, Simplified RF, Ozone impacts . No climate impacts or feedbacks. Newton’s method. Need initial guess and derivative. Quadratic convergence. Proof via . taylor’s. theorem. x_n+1 = . x_n. – f(. x_n. )/f(. x_n. ). Derivation from point-slope y = m*(x – x_0) + y_0:. The dimension of an infinitely “crinkly” line > 1.. It’s “embedding space” is 2 dimensions.. The same can be done with a 2D sheet: infinitely crinkled it has dimension > . 2. .. It’s “embedding space” is 3 dimensions.. by: Saeed . Heidary. 29 Feb 2013. Outline:. Chaos in Deterministic Dynamical systems. Sensitivity to initial conditions. Lyapunov. exponent. Fractal geometry. Chaotic time series prediction. Chaos in Deterministic Dynamical systems. Transformed. Using Geometers Sketchpad. What happens In a . rigid transformation?. Shape changes size and position. Shape changes size but not position. Shape changes position but not size . Shape doesn’t change at all. And out of the ground the . Lord. God made to spring up every tree that is pleasant to the sight and good for food. The tree of life was in the midst of the garden, and the tree of the knowledge of good and evil.(ESV).