doi:10.1016/S0097-8493(98)00039-9 
Copyright © 1998 Elsevier Science Ltd. All rights reserved
Chaos & Graphics
Structure generation by palindromization
Max-Lingner-Str. 5c, D-13189 Berlin, Germany
Available online 13 October 1998.
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Abstract
‘Palindromization' refers to an iterative process in which a starting number N0 is turned into 
by writing its digits in reversed order. Subsequently, N0 and
are added (or subtracted), yielding N1, and the process repeated. Arranging the resulting sequences, Nn, one beneath the other and centered, assigning colors to the digits, we obtain intricate colored patterns. These patterns depend on the starting number, N0, the base g of the chosen number system and the specific kind of succession of additions and subtractions in the palindromization process, called the mode m of palindromization. Various types of structures generated by palindromization are presented: patternless and aperiodic, periodic, mixed types, quasipalindromic trapezia (Sierpinski gaskets), bent repetitive sequences, and columns of substructures looking something like hieroglyphs.
Author Keywords: palindromization process; identical and extended reproduction of sequences; fractals and Sierpinski-gaskets; bent repetitive sequences; trieroglyph chaos
Article Outline
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Fig. 1. Patternless, aperiodic behavior. N0=196, g=10, m=a1.
Fig. 2. Period with repetitive sequences. N0=1089, g=10, m=a1s2(a3s3)2(15 ).(a) Plotting each 15-th sequence; (b) Plotting each 60-th sequence).
Fig. 3. Mixed type: Transition from aperiodic behavior to periodic. N0=1089, g=10, m=s1a6s1a4(12).
Fig. 4. Mixed type: Coexistence of patterns and patternless areas. N0=1089, g=10 ,m=s1a6s3a4(14).
Fig. 5. Similar triangles. N0=1056, g=7, m=a8s9(a2s4)2(29).
Fig. 6. Quasipalindromic trapezium (Sierpinski-gasket). N0=1078, g=9, m=a6s4a6s1(17).
Fig. 7. Bent repetitive sequences. N0=1089, g=10, m=(s2a1)90s1a2(273).
Fig. 8. Columns of substructures, looking something like hieroglyphs. N0=1089, g=10, m=s2a2s2(a2s1)2(a1s1)21s1(55).
Abstract
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