US2014025353A1PendingUtilityA1
Algorithm and a Method for Characterizing Fractal Volumes
Est. expiryJul 13, 2032(~6 yrs left)· nominal 20-yr term from priority
H10W 74/40G06F 17/10G06F 2111/10C09D 163/00G06F 30/23G06F 17/5018
46
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Claims
Abstract
A computer implemented method for obtaining an analytical representation of an internal structure and spatial properties distribution of a selected physical domain includes identifying d-dimensional correspondences of measured spatial properties or field distributions; and applying an inverse algorithm to the d-dimensional spatial properties or field distributions to calculate the Weierstrass-Mandelbrot (W-M) fractal model to thereby determine parameters defining an analytical and continuous Weierstrass-Mandelbrot (W-M) representation.
Claims
exact text as granted — not AI-modifiedWhat is claimed as new and desired to be protected by Letters Patent of the United States is:
1 . A computer implemented method for obtaining an analytical representation of an internal structure and spatial properties distribution of a selected physical domain, comprising:
identifying d-dimensional correspondences of measured spatial properties or field distributions; and applying an inverse algorithm to the d-dimensional spatial properties or field distributions to calculate the Weierstrass-Mandelbrot (W-M) fractal model to thereby determine parameters defining an analytical and continuous Weierstrass-Mandelbrot (W-M) representation.
2 . The method of claim 1 , wherein the physical domain is selected from a metal alloy, a carbon epoxy composite, or a biological tissue.
3 . The method of claim 1 , wherein the physical domain is a man-made structure selected from a microprocessor, an aircraft, a ship, an automobile, a darn, a road layer, a bridge, or a building.
4 . The method of claim 1 , wherein the physical domain is a live organism or part of a live organism or a in vitro version of them (e.g wood).
5 . The method of claim 1 , wherein the physical domain is a digital representation of a real or artificial object.
6 . The method of claim 5 , wherein the digital representation is a spatial distribution of a scalar field within a volume such as magnetic resonance slice images, x-ray tomography data, ultrasonic data trough a volume, or any simulated entity distributed in a volume.
7 . The method of claim 1 , wherein the physical domain is a landform selected from a mountain, a lake, part of a landform, a planet, part of a planet, a solar system, part of a solar system, a cluster of solar systems, part of a cluster of solar systems, a galaxy, part of a galaxy, a cluster of galaxies, or part of a cluster of galaxies.
8 . The method of claim 1 , wherein the d-dimensional modeling is obtained by applying a formula
W
(
r
)
==
γ
M
∑
m
=
1
M
∑
n
=
-
∞
∞
A
m
(
1
-
k
0
γ
n
n
m
·
r
)
φ
mn
(
k
0
γ
n
)
D
-
(
d
+
1
)
,
(
3
)
where n m are d-dimensional unit.
9 . The method of claim 8 , wherein based on an array of measurements over a selected region of the domain, parameters of the d-dimensional W-M fractal model are identified that best fit the array of measurements by decomposing the problem so as to apply singular value decomposition for determining unknown phases of the W-M fractal model.
10 . A computer software product comprising a physical computer-readable medium including stored instructions that, when executed by a computer, cause the computer to:
identify d-dimensional correspondences of measured spatial properties or field distributions; and apply an inverse algorithm to the d-dimensional spatial properties or field distributions to calculate the Weierstrass-Mandelbrot (W-M) fractal model to thereby determine parameters defining an analytical and continuous Weierstrass-Mandelbrot (W-M) representation.
11 . The computer software product of claim 10 , wherein the physical domain is selected from a metal alloy, a carbon epoxy composite, or a biological tissue.
12 . The computer software product of claim 10 , wherein the physical domain is a man-made structure selected from a microprocessor, an aircraft, a ship, an automobile, a dam, a road layer, a bridge, or a building.
13 . The computer software product of claim 10 , wherein the physical domain is a live organism or part of a live organism or a in vitro version of them (e.g wood).
14 . The computer software product of claim 10 , wherein the physical domain is a digital representation of a real or artificial object.
15 . The computer software product of claim 14 , wherein the digital representation is a spatial distribution of a scalar field within a volume such as magnetic resonance slice images, x-ray tomography data, ultrasonic data trough a volume, or any simulated entity distributed in a volume.
16 . The computer software product of claim 10 , wherein the physical domain is a landform selected from a mountain, a lake, part of a landform, a planet, part of a planet, a solar system, part of a solar system, a cluster of solar systems, part of a cluster of solar systems, a galaxy, part of a galaxy, a cluster of galaxies, or part of a cluster of galaxies.
17 . The computer software product of claim 10 , wherein the d-dimensional modeling is obtained by applying a formula
W
(
r
)
==
γ
M
∑
m
=
1
M
∑
n
=
-
∞
∞
A
m
(
1
-
k
0
γ
n
n
m
·
r
)
φ
mn
(
k
0
γ
n
)
D
-
(
d
+
1
)
,
(
3
)
where n m are d-dimensional unit.
18 . The computer software product of claim 17 , wherein based on an array of measurements over a selected region of the domain, parameters of the d-dimensional W-M fractal model are identified that best fit the array of measurements by decomposing the problem so as to apply singular value decomposition for determining unknown phases of the W-M fractal model.Cited by (0)
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