Symmetry & regular patterns
From GenerativeArt
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In other words, symmetry operations are generative systems that can be used to create generative art. | In other words, symmetry operations are generative systems that can be used to create generative art. | ||
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== Symmetry Groups == | == Symmetry Groups == | ||
The codes shown with each illustration are another way of describing the operations that have been applied. Here a number refers to the number of arcs the 360 degrees of a full rotation have been divided into. A single "m" denotes a reflection between the units. A double "mm" denotes a reflection between the units and then a second reflection applied to each resulting unit. | The codes shown with each illustration are another way of describing the operations that have been applied. Here a number refers to the number of arcs the 360 degrees of a full rotation have been divided into. A single "m" denotes a reflection between the units. A double "mm" denotes a reflection between the units and then a second reflection applied to each resulting unit. | ||
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<span style="font-size:larger;text-decoration:underline">The 7 Line Groups</span> | <span style="font-size:larger;text-decoration:underline">The 7 Line Groups</span> | ||
There are only 7 distinct symmetry groups relative to a line. Such a pattern is sometimes called a frieze (say "freeze") as in the architectural formation. The operation codes shown correspond to translation ("t"), reflection ("m"), a 180 degree rotation ("2"), and glide reflection ("tg"). | There are only 7 distinct symmetry groups relative to a line. Such a pattern is sometimes called a frieze (say "freeze") as in the architectural formation. The operation codes shown correspond to translation ("t"), reflection ("m"), a 180 degree rotation ("2"), and glide reflection ("tg"). | ||
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There are only 17 distinct symmetry groups relative to a plane. These are the so called "wallpaper patterns". Here they are by way of examples: | There are only 17 distinct symmetry groups relative to a plane. These are the so called "wallpaper patterns". Here they are by way of examples: | ||
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