Fractal generation, as for video graphic displays
First Claim
Patent Images
1. A method of generating fractals comprising the steps of:
- convolving generator patterns with seed patterns of dots to generate convolution results for each of a plurality of sample spaces, such spaces being consecutively ordinally numbered in order of their successively more sparse sampling;
expanding the convolution results in each of the higher numbered sample spaces through interpolation to a sampling density comparable to that in a lower numbered sample space;
combining samples of the convolution results and the expanded convolution results of similar sampling density on a corresponding sample-by-sample basis; and
carrying out said steps of expanding through interpolation and said steps of combining so as to result in the expanded convolution results of each of the higher numbered sample spaces ultimately being combined with the convolution results in said first sample space, thereby generating said fractals.
1 Assignment
0 Petitions
Accused Products
Abstract
Fractals are generated based on their self-similarity properties. This is done by convolving a basic shape, or "generator pattern", with a "seed pattern" of dots, in each of different spatial scalings. The convolution results are then combined to define a multi-dimensional object, identifiable as a fractal. Two-dimensional sections of this object are used in generating graphic images for video display.
-
Citations
55 Claims
-
1. A method of generating fractals comprising the steps of:
-
convolving generator patterns with seed patterns of dots to generate convolution results for each of a plurality of sample spaces, such spaces being consecutively ordinally numbered in order of their successively more sparse sampling; expanding the convolution results in each of the higher numbered sample spaces through interpolation to a sampling density comparable to that in a lower numbered sample space; combining samples of the convolution results and the expanded convolution results of similar sampling density on a corresponding sample-by-sample basis; and carrying out said steps of expanding through interpolation and said steps of combining so as to result in the expanded convolution results of each of the higher numbered sample spaces ultimately being combined with the convolution results in said first sample space, thereby generating said fractals.
-
-
2. A method of generating a fractal comprising the steps of:
-
providing a seed pattern of dots in each of a a plurality of sample spaces consecutively ordinally numbered first through nth, said first sample space being regularly sampled in a plurality of dimensions, and each other sample space being regularly sampled in those dimensions more sparsely than the sample space with the next lower ordinal number; providing a generator pattern in a normalized sample space; performing a spatial convolution of said generator pattern with the respective seed patterns in each of the sample spaces; expanding, by means of interpolating, the spatial convolution result obtained in each said other sample space to the sampling density of said first sample space and combining the expanded spatial convolution result with the spatial convolution result obtained in said first sample space, to result in said fractal. - View Dependent Claims (3, 4, 5, 6, 7, 8, 9, 10)
-
-
11. A method of generating in sampled form a first raster-scanned video signal comprising the steps of:
-
providing for each field scan a seed pattern of dots in each of a plurality of sample spaces consecutively ordinally numbered first through nth, said first sample space being regularly sampled in a plurality of dimensions, and each other sample space being regularly sampled in those dimensions more sparsely than the sample space with the next lower ordinal number; providing for each field scan a respective generator pattern for each of said plurality of sample spaces consecutively ordinally numbered first through nth ; performing a spatial convolution of each generator pattern with the seed pattern sampled at the same sampling density in accordance with a raster scanning pattern, to obtain for each field scan a convolution result at that respective sampling density; expanding by means of interpolation those convolution results of lower sampling density and combining the convolution results at similar sampling densities; obtaining in response to said expanding and combining steps the combination of those convolution results in a raster-scanned sample space; and converting each level sample of said combination of convolution results to a respective level sample of said first raster-scanned video signal in accordance with an established scheme. - View Dependent Claims (12, 13, 14, 15, 16)
-
-
17. A fractal generator comprising:
-
means for generating raster scanned seed patterns of dots in each of a multiplicity of two-dimensional sample spaces consecutively ordinally numbered first through nth and successively more sparsely sampled; means for defining a generator pattern disposed over an array of grouped pixel locations; means for extracting, from said raster scanned seed patterns in each of said sample spaces, successive arrays of grouped pixel locations similar to that over which said generator pattern is disposed; means for convolving in each sample space said generator pattern array and each successive array of grouped pixel locations from the raster scanned seed pattern in that sample space to obtain a respective convolution result; respective means, associated with each sample space except the first for expanding through interpolation a function sampled in that space to the sampling density of the next lower numbered sampling space; means for deriving from the convolution result in said nth sample space the function which is subsequently expanded through interpolation by said means for expanding a function sampled in said nth space; and respective means for combining in each of said first through (n-1)th sample spaces the convolution result in that sample space with the function expanded through interpolation to the sampling density of that sample space, thereby to generate in each of said second through (n-1)th sample spaces the function sampled in that space which is subsequently expanded through interpolation by said means for expanding a function in that space, and to generate in said first sample space said fractal, which exhibits variation in amplitude. - View Dependent Claims (18, 19)
-
-
20. A method of generating a fractal comprising the steps of:
-
providing a seed pattern of dots in a normalized sample space, which is regularly sampled along spatial coordinates in a plurality of dimensions; providing a generator pattern in said normalized sample space; convolving said generator pattern with said seed pattern to generate convolution results; writing said convolution results into a first memory having storage locations identifiable to respective sets of integral values of said spatial coordinates; expanding at least portions of said convolution results through interpolation in each of said plurality of dimensions, a number of times; writing the once-expanded convolution results into a second memory having storage locations identifiable to respective sets of integral values of said spatial coordinates; writing the plurally-expanded convolution results into respective further memories, each having storage locations identifiable to respective sets of integral values of said spatial coordinates; reading out in parallel scanning successive storage locations in said first, second and further memories, and combining the parallel-scanning read-outs for generating successive samples of the a fractal. - View Dependent Claims (21, 22, 23, 24, 25, 26, 27)
-
-
28. A fractal generator for generating a raster-scanned fractal in sampled-data form that exhibits variation in amplitude, comprising:
-
a plurality of bit-map-organized memories, consecutively ordinally numbered first through nth with respective addressable arrays of storage locations for storing respective fractal components of successively larger scale; respective means for raster scanning each of said bit-map-organized memories in synchronism with the others during a read cycle; means for combining each set of fractal component samples read out in parallel from said plurality of bit-map-organized memories, for each of the successive addresses in their synchronous raster scans, thereby to generate one of the successive samples of said raster scanned fractal in sampled-data form; and means for selectively adjusting the offsets of the respective raster scans of said bit-map-organized memories between each of successive raster scans in their read cycle, relative to order in which the respective fractal components were stored in the addressable arrays of storage locations in said bit-map-organized memories, thereby to animate the generated fractal. - View Dependent Claims (29, 30, 31)
-
-
32. A method of generating a fractal comprising the steps of:
-
providing a seed pattern of dots in a first sample space, which is regularly sampled in a plurality of dimensions; providing a generator pattern; convolving said seed pattern of dots in said first sample space with the generator pattern in said first sample space, thereby to generate spatial convolution results in said first sample space; storing said spatial convolution results in a memory with storage locations mapping said first sample space; selecting portions of said mapped first sample space for retrieval of spatial convolution results to be attributed to other sample spaces ordinally numbered second through nth, n being an integer at least three, each of which other sample spaces is regularly sampled in each of said plurality of dimensions less densely than sample spaces with lower ordinal numbering than its own; expanding, by means of interpolating, the spatial convolution result obtained in each other sample space to the sampling density of said first sample space and combining the expanded spatial convolution result with the spatial convolution result obtained in said first sample space, to result in said fractal. - View Dependent Claims (33, 34, 35)
-
-
36. A method of generating in sampled form a first raster-scanned video signal comprising the steps of:
-
providing, prior to an initial field scan in a sequence of field scans in said video signal, a seed pattern of dots, which dots fall on selected ones of sample locations located periodically in each of the dimensions of one of a plurality of sample spaces, which sample spaces are consecutively ordinally numbered first through nth and are successively more sparsely sampled; providing, prior to an initial field scan in each said sequence of field scans, a generator pattern; performing a spatial convolution of said seed pattern with a generator pattern to obtain sample-data convolution results in a normalized sample space; during each subsequent field scan, re-sampling by raster scan in each of said sample spaces selected portions of the sampled-data convolution results in the normalized sample space, for generating respective convolution results in each of the ordinally numbered sample spaces; during each subsequent field scan, expanding by means of interpolation the selected portions of the convolution results for higher numbered sample spaces to the sampling densities of lower numbered sampled spaces and combining selected convolution results at similar sampling densities; obtaining in response to said expanding and combining steps the combination of those convolution results in a raster-scanned sample space; and converting each level sample of said combination of convolution results to a respective level sample of said first raster-scanned video signal in accordance with an established scheme. - View Dependent Claims (37, 38, 39, 40, 41)
-
-
42. A fractal generator comprising:
-
means for generating a raster scanned seed pattern of dots in the first of a multiplicity of two-dimensional sample spaces consecutively ordinally numbered first through nth and successively more sparsely sampled; means for defining a generator pattern disposed over an array of grouped pixel locations; means for extracting, from said raster scanned seed pattern, successive arrays of grouped pixel locations similar to that over which said generator pattern is disposed; means for convolving in said first sample space said generator pattern array and each successive array of grouped pixel locations from the raster scanned seed pattern in said first sample space to obtain a convolution result for each sample point in said first sample space; means, responding to at least portions of the convolution result for said first sample space, for re-scaling them by resampling to be at the sampling densities of said sample spaces other than the first, to obtain respective convolution results for said other sample spaces; respective means, associated with each sample space except the first for expanding through interpolation a function sampled in that space to the sampling density of the next lower numbered sampling space; means for deriving from the convolution result in said nth sample space the function which is subsequently expanded through interpolation by said means for expanding a function sampled in said nth space; and respective means for combining in each of said first through (n-1)th sample spaces the convolution result in that sample space with the function expanded through interpolation to the sampling density of that sample space, thereby to generate in each of said second through (n-1)th sample spaces the function sampled in that space which is subsequently expanded through interpolation by said means for expanding a function in that space, and to generate in said first sample space said fractal. - View Dependent Claims (43, 44)
-
-
45. A fractal generator comprising:
-
a bit-map-organized memory for storing the first and smallest-in-relative-scale of a plurality, at least three in number, of consecutively ordinally numbered fractal components, respectively of successively larger scale; means multiply raster scanning said bit-map-organized memory on a time-division-multiplex basis during a read-out cycle for supplying a plurality, n in number, of raster-scanned read-out signals; means for adjusting the relative time delays of the first through nth of said memory read-out signals respective to each other; means for expanding, through interpolation, each of the second through nth of the delay-adjusted memory read-out signals, and combining them with the first fractal component for generating samples of raster-scanned fractal, which exhibit variation in amplitude. - View Dependent Claims (46, 47, 48, 49)
-
-
50. A fractal generator comprising:
-
a memory storage dot intensity information in selected ones of its storage locations corresponding to points in a plural-dimensional space; means for raster scanning the storage locations of said memory on a time-division-multiplex basis at successively lower spatial frequencies in each dimension of space to generate a number n at least three of consecutively ordinally numbered memory output signals; a number n of convolvers consecutively ordinally numbered, respectively connected to convolve a generator pattern with the memory output signal having the same ordinal number as its own; means for adjusting the spatial frequency phases, as referred to said first convolver convolution result, the convolution results of each of the other convolvers second through nth ; and means for expanding through interpolation each of the phase-adjusted respective convolution results from the second through nth convolvers to the same sampling density as the convolution results from said first convolver and combining the expanded convolution results with each other and the convolution results from said first convolver, thereby to generate a fractal exhibiting variation in amplitude. - View Dependent Claims (51, 52, 53, 54, 55)
-
Specification