An elementary proof of correctness of the Chaos Game for IFS and its hierarchical and recurrent generalizations

Martyn, Tomasz

doi:10.1016/s0097-8493(02)00092-4

Cited by 4 publications

(5 citation statements)

References 7 publications

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“…M. Professor Barnsley has invented iteration function system IFS (Iterated Function System) in 1985. IFS not only is the description fractal powerful mathematics method, also is the basic tool of fractal graph [ 2 ] . Definition 1. transformation 3 3 :…”

Section: Minute Geometries Principlesmentioning

confidence: 99%

“…Level is the numbers of iteration to control bamboo size, (2) according to the user input the initial parameter value structure initial iteration region, , then the attractor of IFS is the 3D bamboo likes Fig. 1.…”

Section: Algorithms Descriptionsmentioning

confidence: 99%

“…Level is the numbers of iteration to control herb size, (2) according to the user input the initial parameter value structure initial iteration region, Poplar tree's branching pattern belongs to the single axle branching pattern. The peak meristematic tissue long-term maintenance energy, causes the branch to get the advantage the status, the lateral branch obviously is in the inferiority, the lateral branch may produce the next level of lateral branches with the branch by the similar way, thus causes the plant shape to become valuably is tower shaped.…”

Section: Algorithms Descriptionsmentioning

confidence: 99%

“…(1) The user input the initial parameter of poplar tree (for example, level numbers of iteration). Level is the numbers of iteration to control poplar tree size, (2) according to the user input the initial parameter value structure initial iteration region, …”

Section: 12mentioning

confidence: 99%

“…(1) The user input the initial parameter of pear tree (for example, level numbers of iteration). Level is the numbers of iteration to control pear tree size, (2) according to the user input the initial parameter value structure initial iteration region, ..W W also is the compression, according to the theorem 3 W is the compression, then the attractor of this IFS is the 3D fractal bamboo. The same principle may confirm the herb, the poplar tree and pear tree also are the compression.…”

Section: Structures Pear Tree's Affine Transformation Matrixmentioning

confidence: 99%

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Golden Section in 3D Plants IFS Reconstruction

Wang

Zeng

Yan

2008

2008 the 9th International Conference for Young Computer Scientists

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Plants are the important part in the sense of reality of the nature. Plants reconstruction are generally based on two-dimension, use points draw the graph. This paper presents a new method of drawing 3D Plants, the observation indicates the plants like golden section, bifurcate angles of plants such as herbage, pear etc are around 34.4°, poplar's are around 55.6°, they are the golden section of 90°, and the ratio of point of bifurcate to the hole branch is golden section. Combine plant morphology, computer graphics and fractal render 3D plants. Based on the definition of affine change and compress theorem proved plant's compress gene less than 1, 1 ) ( < A r σ ,so the IFS (Iterated Function System) have attractors. According to the results of experiments, present the codes of IFS of some plants. People can skim them in real-time and different point.

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Section: Minute Geometries Principlesmentioning

confidence: 99%

Section: Algorithms Descriptionsmentioning

confidence: 99%

Section: Algorithms Descriptionsmentioning

confidence: 99%

Section: 12mentioning

confidence: 99%

Section: Structures Pear Tree's Affine Transformation Matrixmentioning

confidence: 99%

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