Balancing order and chaos in image generation

Čulík, Karel; Dube, Simant

doi:10.1007/3-540-54233-7_167

Cited by 6 publications

(4 citation statements)

References 16 publications

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“…https://doi.org/10.1017/S0334270000007633 [9] Using fractal geometry for solving divide-and-conquer recurrences 153…”

Section: "(N) =mentioning

confidence: 99%

“…Now we generalize Mutually Recursive Function Systems (MRFS) as studied in [7,9] or Geometric Graph Directed Construction in [15], to condensation MRFS just to facilitate our discussion.…”

Section: Mutually Recursive Function Systemsmentioning

confidence: 99%

“…A condensation MRFS M = (V, C, W, G) is called simply as an MRFS if C = <\>. For many interesting fractal images generated by MRFS see [7,9].…”

Section: Mutually Recursive Function Systemsmentioning

confidence: 99%

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Using fractal geometry for solving divide-and-conquer recurrences

Dube¹

1995

J. Aust. Math. Soc. Series B, Appl. Math

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A relationship between the fractal geometry and the analysis of recursive (divide-andconquer) algorithms is investigated. It is shown that the dynamic structure of a recursive algorithm which might call other algorithms in a mutually recursive fashion can be geometrically captured as a fractal (self-similar) image. This fractal image is defined as the attractor of a mutually recursive function system. It then turns out that the HausdorffBesicovich dimension D of such an image is precisely the exponent in the time complexity of the algorithm being modelled. That is, if the Hausdorff £>-dimensional measure of the image is finite then it serves as the constant of proportionality and the time complexity is of the form &{n D ), else it implies that the time complexity is of the form ®{n D log 7 " n),

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“…https://doi.org/10.1017/S0334270000007633 [9] Using fractal geometry for solving divide-and-conquer recurrences 153…”

Section: "(N) =mentioning

confidence: 99%

“…Now we generalize Mutually Recursive Function Systems (MRFS) as studied in [7,9] or Geometric Graph Directed Construction in [15], to condensation MRFS just to facilitate our discussion.…”

Section: Mutually Recursive Function Systemsmentioning

confidence: 99%

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Using fractal geometry for solving divide-and-conquer recurrences

Dube¹

1995

J. Aust. Math. Soc. Series B, Appl. Math

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“…From our analysis of the decoding of the label and the pointers' dynamics, the fractal approximation developed by the LRAAM seems to have a close relationship with the hierarchical iterated function system model [3,4], where a graph of hierarchical IFS generates the image. In our case, nodes of the graph represent xed points of the pointers' dynamics.…”

Section: Discussionmentioning

confidence: 86%

Encoding pyramids by Labeling RAAM

Lonardi

Sperduti

Starita

Proceedings of IEEE Workshop on Neural Networks for Signal Processing

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In this paper we present preliminary results on the application of Labeling RAAM for encoding pyramids. The LRAAM is a neural network able to develop reduced representations of labeled directed graphs. The capability of such representations to preserve structural similarities is demonstrated on a pyramid. We suggest to exploit this skill in data compression and/or to discover scale ane autosimilarities.

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Iterative devices generating infinite words

Čulík

Karhumäki

1992

Stacs 92

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Balancing order and chaos in image generation

Cited by 6 publications

References 16 publications

Using fractal geometry for solving divide-and-conquer recurrences

Using fractal geometry for solving divide-and-conquer recurrences

Encoding pyramids by Labeling RAAM

Iterative devices generating infinite words

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