Splittig the fractal into three pieces is not difficult.
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Often it is convenient to specify a point as the origin of the coordinate system. The lower left corner can be a good choice, but in general, use any symmetry available, unless there is a compelling reason to do differently.
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
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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 blue and red rulers show the blue and red pieces have altitudes .87 inches, so both have
The green piece has been rotated. To determine the amount of rotation, measure the angle between the green and blue rulers. Both the left and right pictures above give 10 deg, so theta = 10 (left picture) and phi = 10 (right picture). The rotations are counterclockwise, so the angles are positive.
Finally to dtermine the translations, pick a point in the fractal,
say the lower left corner, and measure the horizontal and vertical displacements
of the corresponding points of each of the three pieces. For the green piece, the
lower left corner is in the same location, so
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Here's the IFS table that generated this fractal.
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What's wrong with the e and f values? To answer this question, how does the gasket picture change if you multiple all the e and f values by the same number?
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