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This Concept Map, created with IHMC CmapTools, has information related to: b4. Fractals, Fractals are a class of geometric form The chaotic attractors of flows or invertible maps typically are fractals, A fractal is a pattern that repeats the same design and detail or definition over a broad range of scale. Fractals can be produced by iterated functions An iterated function system (IFS) is a collection of coordinate (pixel) transformations. An IFS will permit scaling transformations, translations, rotations and reflections of the original picture., A fractal is a pattern that repeats the same design and detail or definition over a broad range of scale. ???? Fractals have self-similarity and scale invariance at all levels, Fractals are a class of geometric form ???? Chaos is a class of dynamical behavior., Such repetitions of detail or recurrence of statistically identical geometric patterns in smaller and smaller parts of the original object is the unifying theme of fractals. ???? Fractals deal with geometric patterns, and quantitative and qualitative ways of charactering those patterns., Any piece of a fractal appears the same as it is repeatedly magnified ???? Fractal patterns do not have any characteristic size., A fractal is a pattern that repeats the same design and detail or definition over a broad range of scale. ???? Any piece of a fractal appears the same as it is repeatedly magnified, Chaos, in contrast, deals with time evolution and its underlying or distinguishing characteristics ???? Chaos is a class of dynamical behavior., An iterated function system (IFS) is a collection of coordinate (pixel) transformations. An IFS will permit scaling transformations, translations, rotations and reflections of the original picture. ???? Such repetitions of detail or recurrence of statistically identical geometric patterns in smaller and smaller parts of the original object is the unifying theme of fractals., Fractals are not smooth. They generally look rough, broken, disorganized, jagged, bumpy, or shaggy. Measurements of a fractal object’s length increases as smaller and smaller measures are used to describe it. Therefore, its length in infinite Fractals are of two types., Fractals deal with geometric patterns, and quantitative and qualitative ways of charactering those patterns. ???? Chaos, in contrast, deals with time evolution and its underlying or distinguishing characteristics, b4. Fractals ???? A fractal is a pattern that repeats the same design and detail or definition over a broad range of scale., The chaotic attractors of flows or invertible maps typically are fractals ???? The chaotic attractors of non-invertible maps may or may not be fractals., Fractals deal with geometric patterns, and quantitative and qualitative ways of charactering those patterns. ???? Fractals are a class of geometric form, Fractals are of two types. ???? Natural fractals are found in nature. They are approximate, statistical, or stochastic., A fractal is a pattern that repeats the same design and detail or definition over a broad range of scale. Fractals can be produced by iterated functions Such repetitions of detail or recurrence of statistically identical geometric patterns in smaller and smaller parts of the original object is the unifying theme of fractals., Fractals are generated by many repetitions of a given operation ???? Fractals deal with geometric patterns, and quantitative and qualitative ways of charactering those patterns., Fractals deal with geometric patterns, and quantitative and qualitative ways of charactering those patterns. ???? Fractal objects have non-linear dimensions., Natural fractals are found in nature. They are approximate, statistical, or stochastic. ???? The apparent complexity of the often jagged, irregular, and vaguely self-similar objects of the natural world have simple roots., Fractals have self-similarity and scale invariance at all levels ???? Fractals are generated by many repetitions of a given operation