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Topic: Peano curve

	Peano curve
		In 1880 the Italian logician Giuseppe Peano (1858-1932) constructed the Peano curve, a base motif fractal which uses a line segment as base.
		The fractal dimension of the Peano curve is equal to 2
		Later the name of Peano curve was given to any fractal whose fractal dimension is equal to 2.
	www.2dcurves.com /fractal/fractalpe.html (0 words)

	10.10. Peano, Guiseppe (1858-1932)
		Giuseppe Peano was one of the pioneers in mathematical logic and axiomatization of mathematics.
		Giuseppe Peano was born to a poor farming family in Spinetta, Italy, on August 27, 1858.
		Peano's greatest contributions, however, were in the fields of axiomatization of mathematics and mathematical logic.
	www.shu.edu /projects/reals/history/peano.html (877 words)

	fractal
		The name fractal is derived from the idea that the dimension of such a curve is a fraction of an integer.
		You could say that a fractal is a complex curve, for which a certain amount of similarity can be seen, when magnifying parts of the curve.
		The curves were discovered in the late 17th century, and they shocked the mathematicians of that era.
	www.2dcurves.com /fractal/fractal.html (0 words)

	a fractal - the Peano curve
		Also each floret is composed of tiny sub-florets, and this pattern continues on at least another level below that.
		The fractal at the top of this page, and that also forms the background, is called a Peano curve, discovered by Giuseppe Peano in 1890 and incorporated into fractal theory by Benoit Mandelbrot in 1977.
		Then repeat this process for each of the straight line segments in the path (called the curve even though it's not curvy - don't ask me why).
	www.dace.co.uk /fractal.htm (347 words)

	8.4 The Peano Curve and Fractal Curves
		There are examples of curves (in the sense of continuous maps from the real line to the plane) that completely cover a two-dimensional region of the plane.
		We give a construction of such a Peano curve, adapted from David Hilbert's example.
		the length of the straight pieces being twice the radius of the curved ones.
	www.geom.uiuc.edu /docs/reference/CRC-formulas/node36.html (0 words)

	Drawing a Hilbert Curve
		The explanation linked above is not correct (it shows a picture of a different Peano curve).
		This one is better: http://mathworld.wolfram.com/HilbertCurve.html and shows that the example code does generate two Hilbert curves.
		Note: A Peano curve is ANY curve that fills the entire 2-dimensional plane, so the Hilbert curve is one example of a Peano curve.
	wiki.squeak.org /squeak/1959 (0 words)

	Visual Dictionary of Special Plane Curves
		□ Caustics □ Cissoid (General) □ Conchoid (General) □ Derivative and Integral □ Envelope □ Evolute □ Involute □ Inversion □ Isoptic and Orthoptic □ Parallel Curves □ Pedal Curve □ Radial □ Roulette and Glissette □ Strophoid
		□ line □ circle □ exponential curve □ Spiric Sections □ right strophoid □ Hyperbolic Sine □ Lissajous □ Polynomial □ the Bell Curve (Gaussian Normal curve) □ fractal curves: dragon curve, flowsnake, snowflake, Cantor dust, Peano curve
		□ math of curves (in the works) □ misc curves □ Cusp □ Curvature
	www.xahlee.org /SpecialPlaneCurves_dir/specialPlaneCurves.html (0 words)

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