Measuring IFS Pieces

Scalings

To determine the r scalings of the pieces, isolate some major horizontal feature of the whole shape - say the length of the bottom - and measure the correspondng lengths of the three pieces.

With the blue ruler, we see the bottom of the whole fractal has length 2 inches, say.

The red and blue rulers also show the red and blue pieces have corresponding lengths 1 inch, so they have r = (1 inch)/(2 inches) = 0.5.

The green ruler shows the green piece has bottom length 0.8 inches, so the green piece has r = (0.8 inches)/(2 inches) = 0.4.

To determine the s scalings of the pieces, isolate some major vertical feature of the whole shape - say what would be the altitude if the whole shape were a triangle - and measure the correspondng lengths of the three pieces.

With the black ruler we see the whole fractal has altitude 1.73 inches.

The red and blue rulers show the red and blue pieces have altitudes .87 inches, so both have s = (.87 inches)/(1.73 inches) = 0.5.

The green ruler shows the green piece has altitude 0.7 inches, so for this piece s = (0.7 inches)/(1.73 inches) = 0.4.

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