Super Attractor: Methods for Manifesting a Life beyond Your Wildest Dreams

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Here, l is the data number. An aberration from the attractor can happen in any direction. We describe this using the angles ϑ and φ. Their actual values are random having a uniform distribution on the sphere with the polar and azimuthal angles: Kindermann W. Ergometrie—Empfehlungen für die ärztliche Praxis. Deutsche Zeitschrift für Sportmedizin. 1987;38(6). In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, [2] for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed.

Vieten MM, editor Triple F (F3) Filtering of Kinemaitc Data. ISBS 2004; 2004; Ottawa, Canada: Faculty of Health Science University of Ottawa. Buchthal F, Schmalbruch H. Contraction Times and Fibre Types in Intact Human Muscle. 1970;79(4):435–52.Broscheid KC, Dettmers C, Vieten M. Is the Limit-Cycle-Attractor an (almost) invariable characteristic in human walking? Gait Posture. 2018;63:242–7. pmid:29778064 Clermont CA, Benson LC, Edwards WB, Hettinga BA, Ferber R. New Considerations for Wearable Technology Data: Changes in Running Biomechanics During a Marathon. Journal of Applied Biomechanics. 2019:1–9.

If the evolving variable is two- or three-dimensional, the attractor of the dynamic process can be represented geometrically in two or three dimensions, (as for example in the three-dimensional case depicted to the right). An attractor can be a point, a finite set of points, a curve, a manifold, or even a complicated set with a fractal structure known as a strange attractor (see strange attractor below). If the variable is a scalar, the attractor is a subset of the real number line. Describing the attractors of chaotic dynamical systems has been one of the achievements of chaos theory. A dynamical system is generally described by one or more differential or difference equations. The equations of a given dynamical system specify its behavior over any given short period of time. To determine the system's behavior for a longer period, it is often necessary to integrate the equations, either through analytical means or through iteration, often with the aid of computers. Visual representation of a strange attractor. [1] Another visualization of the same 3D attractor is this video. Code capable of rendering this is available.

RU[ α, β] represents random generation with a uniform characteristic within the interval [ α, β]. With this definition the standard deviation of the random walk depends on the sampling frequency f S. Since the random walk must not be dependent on the specifics of a measurement–the sampling frequency f S -, we introduce a parameter ϕ (random walk’s strength), which does not change with the sampling frequency. Bipedal gait, especially walking, has been the most decisive development of homo sapiens to surpass their ancestors and relatives [ 1]. In the past centuries further cyclic motions like swimming, cycling, rowing or skiing came along, to overcome natural obstacles, to facilitate traveling and then as leisure activities. Recently, cyclic motion descriptions have served as biological templates for developments in robotics together with developments in artificial intelligence [ 2]. Although cyclic movements are performed a thousand-fold each day in everyday life, their underlying composition and structure is not fully understood. RN[1, σ M]( t) represents a normally distributed random element introducing some deviation from a perfect working controlling mechanism. England SA, Granata KP. The influence of gait speed on local dynamic stability of walking. Gait Posture. 2007;25(2):172–8. pmid:16621565