Essays about: "fractals"

Showing result 1 - 5 of 12 essays containing the word fractals.

  1. 1. Probability measures on fractals

    University essay from Uppsala universitet/Matematiska institutionen

    Author : Elvis Schmidt; [2023]
    Keywords : Fractals;

    Abstract : .... READ MORE

  3. 2. Feigenbaum Scaling

    University essay from Linnéuniversitetet/Institutionen för matematik (MA)

    Author : Janek Sendrowski; [2020]
    Keywords : Feigenbaum; Feigenbaum constant; Feigenbaum point; superstable; self-similarity; fractals; final-state diagram; logistic map; period-doubling operator; linearized period-doubling operator; Cantor set; Sharkovsky sequence; Chebyshev interpolation; stable manifold; unstable manifold; orbits; fixed points; scaling factor; pitchfork bifurcation; cobweb plot; renormalization; iterates; one-hump map; unimodal map; bifurcation cascade; Feigenbaum universality; chaos theory; spectrum; generalized Feigenvalues; bifurcation points; superstable points; fixed function; universal function; eigenvalues; eigenvectors; eigenfunctions; universality conditions; Schwarzian derivative; Newton’s method; power method; Arnoldi’s method; attractive fixed point; repellent fixed point; Banach fixed-point theorem; collocation method; functional analysis; topology;

    Abstract : In this thesis I hope to provide a clear and concise introduction to Feigenbaum scaling accessible to undergraduate students. This is accompanied by a description of how to obtain numerical results by various means. READ MORE

  4. 3. How to Avoid Bankruptcy?: Monte Carlo Simulation of Three Financial Markets, using the Multifractal Model of Asset Returns

    University essay from Handelshögskolan i Stockholm/Institutionen för finansiell ekonomi

    Author : Rostislav Sibirtsev; [2019]
    Keywords : Multifractal Model of Asset Returns MMAR ; Simulation; Fractal; Kurtosis; Dependence;

    Abstract : This paper has been an effort to apply fractal mathematics to understanding the general behaviour of financial markets. Fractals are special shapes that look similar at various scales. The specific model used is called the Multifractal Model of Asset Returns (MMAR) - the first ever model used for multifractal financial analysis. READ MORE

  5. 4. Fractal Sets: Dynamical, Dimensional and Topological Properties

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : Nancy Wang; [2018]
    Keywords : logistic function; Cantor set; generalised Cantor Set; fat Cantor set; fractals; fractal dimension; von Koch snowflake; Sierpinski arrowhead curve; Sierpinski carpet; Menger sponge; topological dimension; box dimension; exterior measure; Hausdorff measure; Hausdorff dimension; logistisk funktion; Cantormängd; fet Cantormängd; generaliserade Cantormängd; fraktaler‚; bråktalsdimension; Kochsnöfling; Sierpinskismatta; Sierpinskispilspetskurva; Mengers tvättsvamp; topologiska dimension; lådräkningsdimension; yttre mått; Hausdorffmått; Hausdorffdimension;

    Abstract : Fractals is a relatively new mathematical topic which received thorough treatment only starting with 1960's. Fractals can be observed everywhere in nature and in day-to-day life. To give a few examples, common fractals are the spiral cactus, the romanesco broccoli, human brain and the outline of the Swedish map. READ MORE

  6. 5. Fractals and Billiard Orbits on Sierpinski Carpets

    University essay from Linköpings universitet/Matematiska institutionen

    Author : Erik Landstedt; [2017]
    Keywords : Fractals; Geometry; Billiards; Orbits; Surfaces; Translation surfaces; Homeomorphisms.;

    Abstract : This Bachelor's thesis deals with fractals and orbits on Sierpinski carpets. We present the fundamental theory regarding fractals and some illustrative examples together with fractal billiards. READ MORE