R. P. Taylor

Fractal analysis of Pollock's drip paintings

Scientific objectivity proves to be an essential tool for determining the fundamental content of the abstract paintings produced by Jackson Pollock in the late 1940s. Pollock dripped paint from a can onto vast canvases rolled out across the floor of his barn. Although this unorthodox technique has been recognized as a crucial advancement in the evolution of modern art, the precise quality and significance of the patterns created are controversial. Here we describe an analysis of Pollocks patterns which shows, first, that they are fractal, reflecting the fingerprint of nature, and, second, that the fractal dimensions increased during Pollocks career.

Reversible quantum brownian heat engines for electrons.

Brownian heat engines use local temperature gradients in asymmetric potentials to move particles against an external force. The energy efficiency of such machines is generally limited by irreversible heat flow carried by particles that make contact with different heat baths. Here we show that, by using a suitably chosen energy filter, electrons can be transferred reversibly between reservoirs that have different temperatures and electrochemical potentials. We apply this result to propose heat engines based on mesoscopic semiconductor ratchets, which can quasistatically operate arbitrarily close to Carnot efficiency.

Universal aesthetic of fractals

Abstract Since their discovery by Mandelbrot (The Fractal Geometry of Nature, Freeman, New York, 1977), fractals have experienced considerable success in quantifying the complex structure exhibited by many natural patterns and have captured the imaginations of scientists and artists alike. With ever-widening appeal, they have been referred to both as “fingerprints of nature” (Nature 399 (1999) 422) and “the new aesthetics” (J. Hum. Psychol. 41 (2001) 59). Here, we show that humans display a consistent aesthetic preference across fractal images, regardless of whether these images are generated by natures processes, by mathematics, or by the human hand.

Perceptual and Physiological Responses to Jackson Pollock's Fractals

Fractals have been very successful in quantifying the visual complexity exhibited by many natural patterns, and have captured the imagination of scientists and artists alike. Our research has shown that the poured patterns of the American abstract painter Jackson Pollock are also fractal. This discovery raises an intriguing possibility – are the visual characteristics of fractals responsible for the long-term appeal of Pollocks work? To address this question, we have conducted 10 years of scientific investigation of human response to fractals and here we present, for the first time, a review of this research that examines the inter-relationship between the various results. The investigations include eye tracking, visual preference, skin conductance, and EEG measurement techniques. We discuss the artistic implications of the positive perceptual and physiological responses to fractal patterns.

Reduction of Physiological Stress Using Fractal Art and Architecture

The author reviews visual perception studies showing that fractal patterns possess an aesthetic quality based on their visual complexity. Specifically, people display an aesthetic preference for patterns with mid-range fractal dimensions, irrespective of the method used to generate them. The author builds upon these studies by presenting preliminary research indicating that mid-range fractals also affect the observers physiological condition. The potential for incorporating these fractals into art and architecture as a novel approach to reducing stress is also discussed.

The Construction of Jackson Pollock's Fractal Drip Paintings

Between 1943 and 1952, Jackson Pollock created patterns by dripping paint onto horizontal canvases. In 1999 the authors identified the patterns as fractal. Ending 50 years of debate over the content of his paintings, the results raised the more general question of how a human being could create fractals. The authors, by analyzing film that recorded the evolution of Pollocks patterns as a function of time, show that the fractals resulted from a systematic construction process involving multiple layers of painted patterns. These results are interpreted within the context of recent visual perception studies of fractal patterns.

The role of surface-gate technology for AlGaAs/GaAs nanostructures

Since its first demonstration in 1986, the technique of employing surface-gate designs to define submicrometre-size geometries in the two-dimensional electron gas of AlGaAs/GaAs heterostructures has yielded a wide range of studies of semiconductor physics and novel modes of device operation. To have a future impact in this role, new gate architectures will be required to further develop the techniques ability to tune device geometries through the applied gate bias. Past and future aspects of this system are reviewed in terms of semiconductor physics, technology and device application, and the implications of recent approaches to gate designs are discussed.

Experimental investigation of the breakdown of the Onsager-Casimir relations.

We use magnetoconductance fluctuation measurements of phase-coherent semiconductor billiards to quantify the contributions to the nonlinear electric conductance that are asymmetric under reversal of magnetic field. We find that the average asymmetric contribution is linear in magnetic field (for magnetic flux much larger than 1 flux quantum) and that its magnitude depends on billiard geometry. In addition, we find an unexpected asymmetry in the power spectrum of the magnetoconductance with respect to reversal of magnetic field and bias voltage.

Physical and electrical investigation of ohmic contacts to AlGaAs/GaAs heterostructures

The mechanism by which Ni‐Au‐Ge metallizations establish electrical contact to the two‐dimensional electron gas (2DEG) in modulation‐doped AlGaAs/GaAs heterostructures is investigated. Transmission electron microscopy was used to examine samples after electrical characterization by magnetoresistance measurements at cryogenic temperatures. We present a picture in which a 2DEG of reduced electron density exists under the deposited metallization. The success of the contacting procedure is described in terms of the magnitude of this density and the size, areal density, and penetration depth of a series of metallic spikes which establish the electrical link to the 2DEG. We suggest that the electrical behavior is not dominated by the current injection process at the spike/2DEG interface but is instead dictated by scattering from the array of antidots formed by the spikes and by a dependence of the 2DEG density on the size of the metallic pad. The implications of this picture for future nanostructure devices, fe...

Symmetry of Two-Terminal Nonlinear Electric Conduction

The well-established symmetry relations for linear transport phenomena cannot, in general, be applied in the nonlinear regime. Here we propose a set of symmetry relations with respect to bias voltage and magnetic field for the nonlinear conductance of two-terminal electric conductors. We experimentally confirm these relations using phase-coherent, semiconductor quantum dots.