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Each iteration of the Sierpinski triangle contains triangles related to the next iteration by a scale factor of 1/2. In affine geometry, uniform scaling (or isotropic scaling [1]) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions (isotropically).
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Download QR code; Print/export ... Windows, OS X, Linux, FreeBSD: Adobe Character Animator: ... List of 2D animation software.
The template can accept parameters that describe the size of the object on the screen: |viewport_cm= or |viewport_px=. The template also accepts other geohack parameters to generate the scale argument: dim; type (e.g., "mountain" or "city") population (for type="city" only)
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A scaling can be represented by a scaling matrix. To scale an object by a vector v = (v x, v y, v z), each point p = (p x, p y, p z) would need to be multiplied with this scaling matrix: = []. As shown below, the multiplication will give the expected result: