Abstract: A fractal structure is formed to have a plurality of regions different in fractal dimension characterizing the self-similarity. The fractal structure is grown from one or more origins under growth conditions providing a first fractal dimension in a first portion of the growth process from the start point of time to a first point of time, and under growth conditions providing a second fractal dimension lower than the first fractal dimension in another portion of the growth process from the first point of time to a second point of time. By adjusting the timing for changing the growth conditions, the fractal structure is controlled in nature of phase transition, such as critical temperature for ferromagnetic phase transition, which occurs in the fractal structure. For enhancing the controllability, the first fractal dimension is preferably larger than 2.7 and the second fractal dimension is preferably smaller than 2.3.

Abstract: A fracture structure is grown from a plurality of starting points. A fractal structure, grown from respective starting points and interconnected by interactive growths, forms a neural network. A growth speed originated at a specific starting point is determined by the probability of a material reaching a grown portion from a remote location by means of a diffusion process and the probability of a growth promoting factor reaching a grown portion by means of a diffusion process from a portion grown from a starting point other than the specific one. Anisotropy is introduced into a space in which a fractal structure is to be grown, as required.

Abstract: A fractal structure is formed to have a plurality of regions different in fractal dimension characterizing the self-similarity. Especially in a stellar fractal structure, a region with a low fractal dimension is formed around a core with a high fractal dimension. By adjusting the ratios in volume of these regions relative to the entire fractal structure, the nature of phase transition occurring in the fractal structure, such as a magnetization curve of Mott transition or ferromagnetic phase transition, quantum chaos in the electron state, or the like. For enhancing the controllability, the fractal dimension of the core is preferably larger than 2.7 and the fractal dimension of the region around the core is preferably smaller than 2.3.

Abstract: Phase transition is controlled by controlling fractal dimension of a fractal-coupled structure overall or locally. For a magnetic material, ferromagnetic phase transition temperature of magnetic particles arranged to have self-similarity is controlled by fractal dimension. For a half-filled electron system confined in a treelike fractal, Mott transition is controlled by fractal dimension of the system. Stronger quantum chaos than conventional ones is generated by adding magnetic impurities to the fractal-coupled structure, and through this process, Anderson transition is controlled.

Abstract: An electron device which controls quantum chaos wherein a quantum chaos property is controlled extensively and externally is provided. The electron device which controls quantum chaos is manufactured by using a single material. A heterojunction provided with a first region having an electron system characterized by quantum chaos and a second region having an electron system characterized by integrability is formed. The first region and the second region are adjacent to each other, and the heterojunction is capable of exchanging electrons between the first region and the second region. A quantum chaos property of an electron system in a system formed of the first region and the second region is controlled by applying to the heterojunction an electric field having a component perpendicular to at least a junction surface.

Abstract: An electron device which controls quantum chaos wherein a quantum chaos property is controlled extensively and externally is provided. The electron device which controls quantum chaos is manufactured by using a single material. A heterojunction provided with a first region having an electron system characterized by quantum chaos and a second region having an electron system characterized by integrability is formed. The first region and the second region are adjacent to each other, and the heterojunction is capable of exchanging electrons between the first region and the second region. A quantum chaos property of an electron system in a system formed of the first region and the second region is controlled by applying to the heterojunction an electric field having a component perpendicular to at least a junction surface.

Abstract: An electron device which controls quantum chaos wherein a quantum chaos property is controlled extensively and externally is provided. The electron device which controls quantum chaos is manufactured by using a single material. A heterojunction provided with a first region having an electron system characterized by quantum chaos and a second region having an electron system characterized by integrability is formed. The first region and the second region are adjacent to each other, and the heterojunction is capable of exchanging electrons between the first region and the second region. A quantum chaos property of an electron system in a system formed of the first region and the second region is controlled by applying to the heterojunction an electric field having a component perpendicular to at least a junction surface.

Abstract: In a multiply-complexed one-dimensional structure having a hierarchical structure in which a linear structure as an element of a one-dimensional structure having a finite curvature is made of a thinner one-dimensional structure having a finite curvature, at least two layers of one-dimensional unit structures are bonded in at least one site. For example, in a multiply-twisted helix having a hierarchical structure in which a linear structure as an element of a spiral structure is made of a thinner spiral structure, at least two layers of the unit spiral structures are bonded in at least one site. Alternatively, in a multiply-looped ring structure having a hierarchical structure in which a linear structure as an element of a ring structure is made of a thinner ring structure, at least two layers of ring unit structures are bonded in at least one site.

Abstract: In a multiply-complexed one-dimensional structure having a hierarchical structure in which a linear structure as an element of a one-dimensional structure having a finite curvature is made of a thinner one-dimensional structure having a finite curvature, at least two layers of one-dimensional unit structures are bonded in at least one site. For example, in a multiply-twisted helix having a hierarchical structure in which a linear structure as an element of a spiral structure is made of a thinner spiral structure, at least two layers of the unit spiral structures are bonded in at least one site. Alternatively, in a multiply-looped ring structure having a hierarchical structure in which a linear structure as an element of a ring structure is made of a thinner ring structure, at least two layers of ring unit structures are bonded in at least one site.

Abstract: A fractal structure is formed to include at least one heterojunction formed by two regions different in fractal dimension characterizing the self similarity from each other. Especially in a stellar fractal structure, the heterojunction is formed by forming a region (dendritic region) with a lower fractal dimension around a core (somatic region) with a higher fractal dimension. These two regions forming the heterojunction are different in phase from each other. For example, they are a combination of a ferromagnetic phase and a paramagnetic phase, or a combination of a metal phase and a Mott insulative phase. The fractal structure may be used to realize a functional material or a functional device.

Abstract: In a multiply-twisted helix including having a hierarchical structure in which a linear structure as an element of a particular spiral structure is made of a thinner spiral structure, the spiral structures being bonded in at least one site at least between two layers, and the number of turns of the spiral structure of the lowest layer being N, the interval of bonds between m-th degree layers in the multiply-twisted helix is determined by the power function Ng(m) of N having an arbitrary linear function g(m)=&bgr;m+&ggr; (where &bgr; and &ggr; are constant values and &ggr;≠0) of m as its exponent.

Abstract: An image processing apparatus capable of extracting widely viewed features of an entire image and speedily performing image processing, and a method and an information recording medium for such processing. Image data of an original image is obtained by imaging the entire original image with an image pickup unit at a time. An amplitude distribution of a signal is obtained from the image data by fast Fourier transform performed by a fast Fourier transform section of a signal processing unit. An amplitude replacement section replaces the amplitude distribution with a predetermined function using the distance from a center of a frequency plane as a parameter. An inverse fast Fourier transform section forms an image corresponding to the original image by inverse fast Fourier transform from a phase distribution of points obtained by the fast Fourier transform and from an amplitude distribution obtained by the above-described replacement.

Abstract: To obtain good approximate solutions of a combinatorial optimization problem such as traveling salesman problem and to enable its processing apparatus in form of massively parallel exclusive devices, an information carrier corresponding to the distribution of a plurality of points given on an n-dimensional space (n is an integer not smaller than 2), and time development and time reversal of the information carrier are used to process the information. The information carrier may be the density of particles or optical intensity corresponding to the distribution of the given points, and a diffusion process of the particles or a defocusing process is used as changes with time. The traveling salesman problem is solved by using this method.

Abstract: In a multiply-complexed one-dimensional structure having a hierarchical structure in which a linear structure as an element of a one-dimensional structure having a finite curvature is made of a thinner one-dimensional structure having a finite curvature, at least two layers of one-dimensional unit structures are bonded in at least one site. For example, in a multiply-twisted helix having a hierarchical structure in which a linear structure as an element of a spiral structure is made of a thinner spiral structure, at least two layers of the unit spiral structures are bonded in at least one site. Alternatively, in a multiply-looped ring structure having a hierarchical structure in which a linear structure as an element of a ring structure is made of a thinner ring structure, at least two layers of ring unit structures are bonded in at least one site.

Abstract: An optical and/or electronic device is operated by degeneracy of density of states caused by confinement of electrons in a fractal region having a self-similarity. An AlGaAs/GaAs light emitting device is configured by distributing GaAs quantum dots in a fractal arrangement and confining them in i-type AlGaAs. A single-electron state of the quantum dot array exhibits degeneracy of density of states. Further, a strong quantum chaos is generated to bring about degeneracy of density of states by applying a random magnetic field by addition of a magnetic impurity to the region having a self-similarity.

Abstract: A fractal structure is formed to have a plurality of regions different in fractal dimension characterizing the self-similarity. The fractal structure is grown from one or more origins under growth conditions providing a first fractal dimension in a first portion of the growth process from the start point of time to a first point of time, and under growth conditions providing a second fractal dimension lower than the first fractal dimension in another portion of the growth process from the first point of time to a second point of time. By adjusting the timing for changing the growth conditions, the fractal structure is controlled in nature of phase transition, such as critical temperature for ferromagnetic phase transition, which occurs in the fractal structure. For enhancing the controllability, the first fractal dimension is preferably larger than 2.7 and the second fractal dimension is preferably smaller than 2.3.

Abstract: A fractal structure is formed to have a plurality of regions different in fractal dimension characterizing the self-similarity. Especially in a stellar fractal structure, a region with a low fractal dimension is formed around a core with a high fractal dimension. By adjusting the ratios in volume of these regions relative to the entire fractal structure, the nature of phase transition occurring in the fractal structure, such as a magnetization curve of Mott transition or ferromagnetic phase transition, quantum chaos in the electron state, or the like. For enhancing the controllability, the fractal dimension of the core is preferably larger than 2.7 and the fractal dimension of the region around the core is preferably smaller than 2.3.

Abstract: A nonlinear coupling oscillator array is configured in such a manner that, for example, two layers in each of which a number of quantum dots as oscillators are arranged two-dimensionally are laid one on another. Adjacent quantum dots in the upper layer have tunnel coupling that exhibits a nonlinear current-voltage characteristic. The quantum dots in the upper layer receive an input of initial data/bias current, and each quantum dot in the upper layer is coupled with one quantum dot in the lower layer via a gate function having a time constant. Adjacent quantum dots in the lower layer do not interact with each other and the quantum dots in the lower layer are connected to the ground. For example, initial data are input by generating electron-hole pairs by applying light having an intensity profile corresponding to data, and injecting resulting electrons into the quantum dots of the upper layer.

Abstract: An image processing apparatus capable of extracting widely viewed features of an entire image and speedily performing image processing, and a method and an information recording medium for such processing. Image data of an original image is obtained by imaging the entire original image with an image pickup unit at a time. An amplitude distribution of a signal is obtained from the image data by fast Fourier transform performed by a fast Fourier transform section of a signal processing unit. An amplitude replacement section replaces the amplitude distribution with a predetermined function using the distance from a center of a frequency plane as a parameter. An inverse fast Fourier transform section forms an image corresponding to the original image by inverse fast Fourier transform from a phase distribution of points obtained by the fast Fourier transform and from an amplitude distribution obtained by the above-described replacement.

Abstract: An image processing apparatus capable of extracting widely viewed features of an entire image and speedily performing image processing, and a method and an information recording medium for such processing. Image data of an original image is obtained by imaging the entire original image with an image pickup unit at a time. An amplitude distribution of a signal is obtained from the image data by fast Fourier transform performed by a fast Fourier transform section of a signal processing unit. An amplitude replacement section replaces the amplitude distribution with a predetermined function using the distance from a center of a frequency plane as a parameter. An inverse fast Fourier transform section forms an image corresponding to the original image by inverse fast Fourier transform from a phase distribution of points obtained by the fast Fourier transform and from an amplitude distribution obtained by the above-described replacement.