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?
Begin by selecting a fractal from the top menu. Your choices are:
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.
Stepping through the stages:
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
Choose a fractal from the top menu or create your own.
Observe how the fractal image and table values change as you step
through the various stages.
How does the image change with each step? If you step one stage
forward, what about the fractal image changes and what stays the same?
Fractals have a property called self-similarity. This
means every part of the fractal looks like the whole fractal. Looking at
the highest stage of your fractal, try to find parts that look like the
whole. How many can you find?
As you go from Stage 0 to Stage 1, how many times is the Now/Next
rule applied? from Stage 1 to Stage 2? 2 to 3? Can you see how this is
reflected in the table values?
When the table rows turn blue, the fractal image will not change anymore. What would the image look like in the next stage?
Looking at the table, see if you can answer the following questions:
If you would like to rate this lesson, then please register. Riuscipisci bla feummod
olenim dignit irit luptatum zzriliquamet la commodigna facilit prat.