Fractal Tool

  • Fractal Tool


    Play with shapes that grow, shrink, and change over several stages. Explore self-similarity and patterns in fractal measurements. Can you see how these shapes are fractals? 




    3511 Snowflake3511 Tree3511 Square3511 Triangle3511 Blank
    Koch SnowflakeFractal TreeReduced SquareSierpinski TriangleCreate your Own


    Initial, Now, and Next images are shown below the work area. Initial is the original shape (Stage 0) from which a fractal will be created. Now and Next describe the process that will be used to create the fractal. Any element that looks like Now at the current stage will be transformed to Next in the following stage.

    How to Use

    Stepping through the stages:

    • To step through the stages of your fractal, use the + and buttons. The fractal will move 1 stage forwards or backwards, and the table to the right of the work area will be updated.
    • The PLAY button automatically steps through all stages, starting with the current stage.
    • The RESET button resets the current fractal to Stage 0 (the image shown in the Initial image).

    Note: Each fractal will be animated for the first several stages only, due to computer limitations. However, statistics about stages beyond those shown graphically will appear in the table to the right. The orange rows represent those stages for which the image can be displayed; the blue rows represent those stages for which there are no images.