The Beauty of Fractals: Six Different Views
Denny Gulick, Jon Scott
MAA, 2010 - Electronic books - 95 pages
With the coming of the computer age, fractals have emerged to play a significant role in art images, scientific application and mathematical analysis. The Beauty of Fractals is in part an exploration of the nature of fractals, including examples which appear in art, and in part a close look at famous classical fractals and their close relatives. The final essay examines the relationship between fractals and differential equations. The essays that appear in The Beauty of Fractals contain perspectives different enough to give the reader an appreciation of the breadth of the subject. The essays are self-contained and expository, and are intended to be accessible to a broad audience that includes advanced undergraduate students and teachers at both university and secondary-school level. The book is also a useful complement to the material on fractals which can be found in textbooks.
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ˇ ˇ 3-body problem ├ C ┬ affine hull binary fractal trees binary tree branching angles Calculus Cantor set chaos game child nodes contraction defined Devaney dynamics edge Editor equation equilateral triangle example fern flower fractal 781 fractal dimension Fractal Geometry fractal PQR Fractal Skewed golden gnomon golden Koch golden ratio golden triangle graph Hamiltonian systems infinite number inflorescences Koch curve Koch Snowflake L-System length Level 1 Level line segment Mandelbrot set matrix orbits oriented area parallelogram pentagon phase space plane plant Poincar┤e point x;y reach the Fail recursion root node rotation rule table scaling self-contacting symmetric binary self-contacting trees self-similar sequence side Sierpi┤nski Carpet Sierpi┤nski Triangle sin┬ square stage subtree symmetric binary fractal symplectic integration symplectic integration algorithm symplectic maps systems of ODEs T.rsc tetrahedron Theorem Thomasina trees with branching trilinear 3-body problem trunk Undergraduate Mathematics vector vertex vertical volume