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- H_tree abstract "The H tree (so called because its repeating pattern resembles the letter "H") is a family of fractal sets whose Hausdorff dimension is equal to 2. They can be constructed by starting with a line segment of arbitrary length, drawing two shorter segments at right angles to the first through its endpoints, and continuing in the same vein, reducing (dividing) the length of the line segments drawn at each stage by √2. Surprisingly, continuing this process will eventually come arbitrarily close to every point in a rectangle, or in other words, the H-fractal is a space-filling curve. It is also an example of a fractal canopy, in which the angle between neighboring line segments is always 180 degrees.An alternative process that generates the same fractal set is to begin with a rectangle with sides in the ratio 1:√2, known as a "silver rectangle", and repeatedly bisect it into two smaller silver rectangles, at each stage connecting the two centroids of the two smaller rectangles by a line segment. A similar process can be performed with rectangles of any other shape, but the silver rectangle leads to the line segment size decreasing uniformly by a √2 factor at each step while for other rectangles the length will decrease by different factors at odd and even levels of the recursive construction.The Mandelbrot Tree is a very closely related fractal using rectangles instead of line segments, slightly offset from the H-tree positions, in order to produce a more naturalistic appearance. To compensate for the increased width of its components and avoid self-overlap, the scale factor by which the size of the components is reduced at each level must be slightly greater than √2.".
- H_tree thumbnail H_tree.svg?width=300.
- H_tree wikiPageExternalLink 26932.
- H_tree wikiPageExternalLink fm13.html.
- H_tree wikiPageExternalLink e125113.
- H_tree wikiPageExternalLink e223901.
- H_tree wikiPageExternalLink BerEpp-SCG-93.pdf.
- H_tree wikiPageExternalLink index.htm.
- H_tree wikiPageID "11333082".
- H_tree wikiPageRevisionID "588447267".
- H_tree hasPhotoCollection H_tree.
- H_tree title "H-Fractal".
- H_tree title "Mandelbrot Tree".
- H_tree urlname "H-Fractal".
- H_tree urlname "MandelbrotTree".
- H_tree subject Category:Clock_signal.
- H_tree subject Category:Fractals.
- H_tree subject Category:Trees_(data_structures).
- H_tree type Abstraction100002137.
- H_tree type Cognition100023271.
- H_tree type Form105930736.
- H_tree type Fractal105931152.
- H_tree type Fractals.
- H_tree type PsychologicalFeature100023100.
- H_tree type Structure105726345.
- H_tree comment "The H tree (so called because its repeating pattern resembles the letter "H") is a family of fractal sets whose Hausdorff dimension is equal to 2. They can be constructed by starting with a line segment of arbitrary length, drawing two shorter segments at right angles to the first through its endpoints, and continuing in the same vein, reducing (dividing) the length of the line segments drawn at each stage by √2.".
- H_tree label "H tree".
- H_tree label "H-Baum".
- H_tree sameAs H-Baum.
- H_tree sameAs m.02r80qp.
- H_tree sameAs Q1562440.
- H_tree sameAs Q1562440.
- H_tree sameAs H_tree.
- H_tree wasDerivedFrom H_tree?oldid=588447267.
- H_tree depiction H_tree.svg.
- H_tree isPrimaryTopicOf H_tree.
