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Tupper's self-referential formula - Wikipedia

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Tupper's self-referential formula is a formula that visually represents itself when graphed at a specific location in the (x, y) plane. The formula was defined by Jeff Tupper and appears as an example in his 2001 SIGGRAPH paper on reliable two-dimensional computer graphing algorithms.[1] This paper discusses methods related to the GrafEq formula-graphing program developed by Tupper.[2] The formula is an inequality defined as: 1 2 < ⌊ m o d ( ⌊ 𝑦 17 ⌋ 2 − 17 ⌊ 𝑥 ⌋ − m o d ( ⌊ 𝑦 ⌋ , 17 ) , 2 ) ⌋ where ⌊ … ⌋ denotes the floor function, and mod is the modulo operation. Let 𝑘 equal the following 543-digit integer: Graphing the set of points ( 𝑥 , 𝑦 ) in 0 ≤ 𝑥 < 106 and 𝑘 ≤ 𝑦 < 𝑘 + 17 which satisfy the formula, results in the following plot:[note 1] The formula is a general-purpose method of decoding a bitmap stored in the constant 𝑘 , and it could be used to draw any other image. When applied to the unbounded positive range 0 ≤ 𝑦 , the formula tiles a vertical swath

Tupper's self-referential formula - Wikipedia Jump to content From Wikipedia, the free encyclopedia Formula that visually represents itself when graphed Tupper's self-referential formula is a formula that visually represents itself when graphed at a specific location in the ( x , y ) plane. History [ edit ] The formula was defined by Jeff Tupper and appears as an example in his 2001 SIGGRAPH paper on reliable two-dimensional computer graphing algorithms. &#91; 1 &#93; This paper discusses methods related to the GrafEq formula-graphing program developed by Tupper. &#91; 2 &#93; Formula [ edit ]

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