Fractals for the classroom: strategic activities
Springer-Verlag, 1991 - 128 pages
This first volume of strategic activities is designed to develop through a hands-on approach, a basic mathematical understanding and appreciation of fractals. The concepts presented on fractals include self-similarity, the chaos game, and complexity as it relates to fractal dimension. These strategic activities have been developed from a sound instructional base, stressing the connections to the contemporary curriculums recommended in the National Council of Teachers of Mathematics' Curriculum and Evaluation Standards for School Mathematics. Where appropriate the activities take advantage of the technological power of the graphics calculator. These activites make excellent extensions to many of the topics that are already taught in the current curriculum. Together, they can be used as a complete unit or as the beginning for a semester course on fractals.
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24 32 Boxcount Activity Sheets algorithm appear area at stage box dimension branches Cantor set cellular automata chaos game coloring look-up table completed tree CONNECTIONS construction process contain corresponding Count the number dots endpoints entries exact replica exponential function final stage finite fractal dimension fractal shape geometric sequence given stage graphing calculator grid Implicit Discoveries infinitum iterative process Koch curve Koch snowflake large without bound line segment linear graph logy Mandelbrot set mathematics midpoints move halfway number of pixels number of rolls number of shaded number of triangles number patterns Pascal's triangle path pixels lit power function power relationship random self-similarity dimension Sierpinski tetrahedron Sierpinski triangle slope Specific Directions Stage 2 Stage stage-2 triangle standard graph paper straight line strategic activities strictly self-similar string subsquares subtriangles successive stages tree diagram triangle address underlying University of Bremen variables vertex vertical visual