Richard Taylor
Professor of Physics, Psychology, and Art
Director, Materials Science Institute

Department of Physics
University of Oregon
Eugene, OR 97403-1274, U.S.A.
Tel: +1-541-346-4741
Fax: +1-541-346-3422


Fractals in Nanoelectronics, Retinal Implants and Solar Cells:


Fractal circuit

Artificial neurons:  these fractal circuits are being developed within the Retinal Implant Project in collaboration with Professor Simon Brown at Canterbury University, New Zealand.



Fractal Retinal Implants:













Fractal Solar Cells:





Fractal Nano Circuits:




Film-Boiling LIquids:



Ballistic Optical Devices:





Ballistic Electronic Devices:

Nanoelectronic devices approach one billionth of a meter in size (50,000 times smaller than a human hair). Smaller than today’s commercial devices and made from purer materials, nano-devices are expected to revolutionize the technologies that underpin society.

Ballistic nanoelectronic devices are made from materials so pure that the electrical current travels through the solid much like bullets fly through the air!  Although impurities in the material are minimized in these devices, they have a profound effect on device performance. My research investigates how impurities induce chaos in the electricity by scattering the flow of electrons in the current. This chaotic scattering causes the electricity to flow along fractal patterns through the devices, much like a river splitting into fractal tributaries. Intriguingly, quantum mechanics allows the electrons to behave both like waves and particles, resulting in the highly topical phenomenon ‘quantum chaos’. My research of quantum chaos and the resulting fractal electricity is aimed at understanding the basic principles of electricity at the nano-scale and also how to exploit this novel behavior to produce faster and more powerful electronic devices.

Given that electricity wants to flow along fractal pathways, we are building devices that connect together to form fractal shapes. These fractal circuits are constructed using two “self-assembly” growth processes: one process deposits gold nanoparticles onto tangled DNA strands, the other grows ‘nanoflower’ circuits from nanoclusters (see left image). Self-assembly represents an efficient and  ‘green’ approach to constructing devices. In addition to novel fractal transistors and sensors, we are developing fractals circuits for retinal implants and solar cells. In each case, we use the principle of biomimicry to exploit the functionality of nature’s fractals to provide technological advances. Whereas the fractal circuits mimic neurons for the retinal implants, they replicate the light-harvesting properties of trees for the solar cells.  These two projects represent the most important targets for future physics research – safeguarding human health and the Earth’s environment. For example, the retinal implants are designed to restore vision to the millions of people who are diagnosed each year with retinal diseases that cause loss of vision.

Selected Recent Publications And Media

 “Artificial Vision: Vision of Beauty” Feature Article Physics World 22 (May 2011)
As sensors in digital cameras fast approach the 127 megapixels of the human eye, clinical trials are under way to
implant this technology directly into the retina. But Richard Taylor cautions that such devices must be adapted for
humans, because of the special nature by which we see.


Artificial Retinas Project Movie. Richard Taylor, head of the Artificial Retinas Project, discusses project research. Movie produced by Matt Alpert.


Artificial Retinas Project Radio (mp3 file) Download


"Effect of Fractal Silver Electrodes on Charge Collection and Light Distribution in Semiconducting Organic Polymer Films”, to be published in the Journal of Materials Chemistry A

"The Role of Fractal Patterns on New Materials for Solar Energy Applications: Inorganic Cluster, Films and Fractal Geometry Simulations" Research Corporation for Science Advancement. To be posted.

"Organic Fractals as a Promising Geometry for Enhanced Solar Energy Conversion (2011)" Research Corporation for Science Advancement. To be posted.

 “Fractal Electronic Circuits Self-Assembled From Sb Atomic Clusters” Nanotechnology 22 365304 (2011)

“Toward Chaotic Electron Transport in Bismuth nanocluster wires” Proc. APS meeting (2009)

“Coulomb Blockade in DNA-templated, Quasi-1D Nanoparticle Arrays” (in preparation)

“Self-Propelled Film-boiling Liquids” Physical Review Letters 96 154502 (2006)

“An Optical Demonstration of Fractal Geometry” The Bridges Proceedings Tarquin books 349 (2010)

“Electromagnetic Wave Chaos in Gradient Refractive Index Optical Cavities” Physical Review Letters 86 5466 (2001)

“Effects of Geometric Wave Chaos on the Electromagnetic Eigenmodes of Gradient-index Optical Cavity” Physical Review E 64 026203 (2001)

"Is it the Boundaries or Disorder that Dominates Electron Transport in Semiconductor 'Billiards'?" Fortschr. Phys. 61, 332 (2013)

“Probing the Sensitivity of Electron Wave Interference to Scattering-Induced Disorder in Solid-state Devices” Physical Review B 85 195319 (2012)

“The Impact of Small-Angle Scattering on Ballistic Transport In Quantum Dots” Physical Review Letters 108 196807 (2012)

“Field-oriented Dependence of the Zeeman Spin Splitting in GaInAs Quantum Point Contacts” Physical Review B 81 041303 (2010)

“Investigation of Electron Wave Hybridization in GaInAs/InP Arrays” Applied Physics Letters 95 182105-1-3 (2009)

“Enhanced Zeeman Splitting in GaInAs Quantum Point Contacts” Applied Physics Letters 93 012105 (2008)

“Confinement Properties of a GaInAs/InP Quantum Point Contact” Physical Review B 77 155309 (2008)

“A Unified Model of Electron Quantum Interference For Ballistic and Diffusive Semiconductor Devices” Physical Review B 73 195318-1-7 (2006)

“Experimental Investigation of the Breakdown of the Onsager-Casimir Relations” Physical Review Letters 96 116801 (2006)

“Symmetry of Magnetoconductance Fluctuations of Quantum Dots in the Nonlinear Response Regime” Physical Review B 73 235321(2006)

“Symmetry of Two Terminal Nonlinear Electric Conductance” Physical Review Letters 92 046803-1 (2004)

“Three Key Questions on Fractal Conductance Fluctuations: Dynamics, Quantization and Coherence” Physical Review B 70 085302 (2004)

“A Review of Fractal Conductance Fluctuations in Ballistic Semiconductor Devices” Invited chapter to the book Electron Transport in Quantum Dots Kluwer Academic/Plenum (2003)

“The Dependence of Fractal Conductance Fluctuations on Soft-wall Profile in a Double-layer Billiard” Applied Physics Letters 80 4381 (2002)

“Reversible Quantum Brownian Heat Engines for Electrons” Physical Review Letters 89 116801 (2002)

“The Evolution of Fractal Patterns during a Classical-Quantum Transition” Physical Review Letters 87 036802 (2001)

Metrology of low-disorder self-assembled nanostructures, ONR PowerPoint presentation, August 18, 2011.