PPT-Fractals and Self-Similarity

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 . 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. Amgad. Hussein, Maria . Tokarska. , Edward . Grinko. , . Dimitar. . Atassanov. , Megan Varghese, Emilio . Asperti. GEOMETRY. "Clouds are not spheres, mountains are not cones, coastlines . are not . 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.. Modelling. Fractals. Fractals. A fractal is a mathematical set that typically displays self-similar . patterns. Fractals . may be exactly the same at every scale, . or they . may be nearly the same at different scales. Ferran Pérez de la Cruz i Yeray Rodríguez Bejarano. Itinerary. Introduction. Activities. Simulating Natural Objects and some fractal applications. Activities. Some fractals application. Introduction. 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). . Corpora and Statistical Methods. Lecture 6. Semantic similarity. Part 1. Synonymy. Different phonological. /orthographic. words. highly related meanings. :. sofa / couch. boy / lad. Traditional definition:. these theories have explanatory power domains partially role of relational judgments. Previous structural and aspects of notion of relational similarity by the fact that and her some ways there is in Warm Up. 1.. . If . ∆. QRS.  . ∆. ZYX. , identify the pairs of congruent angles and the pairs of congruent sides.. Solve each proportion.. 2.. . 3.. . . x . = 9. x . = 18. . Q. Word . Similarity: . Distributional Similarity (I). Problems with thesaurus-based . meaning. We don’t have a thesaurus for every language. Even if we do, . they have problems with . recall. M. any . 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. 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.. Warm Up. Solve each proportion.. 1.. . . 2.. . 3.. 4. . If . ∆. QRS . ~ . ∆. XYZ. , identify the pairs of congruent angles and write 3 proportions using pairs of corresponding sides.. . Sketching, Locality Sensitive Hashing. SIMILARITY AND DISTANCE. Thanks to:. Tan, Steinbach, . and Kumar, “Introduction to Data Mining”. Rajaraman. . and . Ullman, “Mining Massive Datasets”. Similarity and Distance.