My Work:
Data Lead, Consultant
Bright Power, Inc.
February 2019 - January 2020
Data Scientist
BrightForge Technology Holdings
October 2017 - June 2018
Consulting Director
Forensic Mathematics Services
Mathematical Analysis for Malpractice
January 2014 - January 2018
Director of Research & Development
Brothers Technology, LLC
Intellectual Property, Research & Development
July 1994 - Present
Senior Consultant, Application Systems
Penguin Random House
Publishing
July 2014 - June 2015
Guest Editor
The Real Life Survival Guide (NPR)
Media Industry
August 2011 - August 2014
Scholar at Large
Citizen Scientists League
Research/Education
July 2012 - February 2014
Director of Technology
The Country School
Primary/Secondary Education Industry
July 2002 - June 2011
Consultant
Yale Mathematics Department
Higher Education Industry
June 2001 - May 2007
Contents:
 | Bio | | In the News | |
| Patents | | Articles | |
| Publications | | Professional Service | |
| Presentations | | References | |
| Music | | Related Links | |
| Multimedia
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A technology developer and inventor with successful designs that run the gamut from an encryption-based Event Verification System (bought by a pre-eminent IP firm) to an automatic household water alarm (licensed to Salton, Inc.). A published mathematician and researcher with numerous journal articles related to number theory and the fractal geometry. Experienced Director of Technology, project manager, inventor, educator, researcher, writer, programmer, and technical design consultant. Possesses a unique, cross-disciplinary background as a problem solver, creative thinker, and effective communicator.
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Data-Conditioned Encryption Method (Provably secure encryption system. Patent No. 8,712,040) |
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Event Verification System (EVS™/Vericam™, Patent No. 5,799,083) |
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Interior Mailbox Light (Postlite™, Patent No. 5,975,713) |
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Portable Ashtray (SmokeMate™, Patent No. 5,673,709) |
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Luminous Pull-Cord (Opticord™, Patent No. 5,454,056) |
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Household Safety Receptacle (Digisafe™, Patent No. 5,320,545) |
Publications:
(Reprints and preprints available upon request)
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H. J. Brothers, "The Nature of Fractal Music," in Benoit Mandelbrot - A Life in Many Dimensions, edited by Michael Frame, World Scientific Publishing (May, 2015).
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N. Neger and H. J. Brothers, "Benoit Mandelbrot: Educator," in Benoit Mandelbrot - A Life in Many Dimensions, edited by Michael Frame, World Scientific Publishing (May, 2015).
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M. F. Barnsley, M. Berry, M. Frame, I. Stewart, D. Mumford, K. Falconer, R. Eglash, H. J. Brothers, N. Lesmoir-Gordon, J. Barrallo, Glimpses of Benoît Mandelbrot (1924-2010). Notices of the American Mathematical Society, Vol. 8, No. 59, 2012; pages |
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H. J. Brothers, Pascal's prism. The Mathematical Gazette, Vol. 96, No. 536, 2012; pages |
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H. J. Brothers, Pascal's triangle: The hidden stor-e. The Mathematical Gazette, Vol. 96, No. 535, 2012; pages |
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H. J. Brothers, Finding e in Pascal's triangle. Mathematics Magazine, Vol. 85, No. 1, 2012; page 51.
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H. J. Brothers, Mandel-Bach Journey:
A marriage of musical and visual fractals. Proceedings of Bridges Pecs, 2010; pages |
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H. J. Brothers, Intervallic scaling in the Bach cello suites. Fractals, Vol. 17, No. 4, 2009; pages 537-545. (Supplementary material)
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H. J. Brothers, How to design your own pi to e converter. |
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H. J. Brothers, Structural scaling in Bach's cello suite no. 3. Fractals, Vol. 15, No. 1, 2007; |
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H. J. Brothers, Improving the convergence of Newton's series approximation for e. College Mathematics Journal, Vol. 35, No. 1, 2004; (The above article appears with permission of CMJ. Supplementary material can be found here.) |
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J. A. Knox and H. J. Brothers, Novel series-based approximations to e. College Mathematics Journal, Vol. 30, No. 4, 1999; pages (NOTE: The above paper was selected by mathematicians Ron Larson, Robert P. Hostetler, and Bruce H. Edwards as one of the fifty best articles on calculus from MAA periodicals. It appears as a supplement to their textbook, Calculus with Analytic Geometry, Seventh Edition.) |
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H. J. Brothers and J. A. Knox, New closed-form approximations to the Logarithmic Constant e. The Mathematical Intelligencer, Vol. 20, No. 4, 1998; pages |
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Mandel-Bach Journey: A Marriage of Musical and Visual Fractals, Bridges Conference, Pecs, Hungary, July 28, 2010. |
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Fractals and Music, The MathScience Innovation Center, Richmond, VA, August 16, 2007. |
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Fractal Music Lab: A Modern Approach to the Mensuration Canon, Norwalk Community College, Norwalk, CT, March 28, 2006. |
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Fractal Music, Mathematical Association of Two-Year Colleges in Connecticut, North Haven, CT, April 29, 2005. |
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Rubbing Shoulders With Newton: A New Look at a Fundamental Constant of Nature, Society for Amateur Scientists, 3rd Annual Meeting, Las Vegas, NV, January 14, 2005. |
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Fractal Music Lab, Yale University Workshop on Fractal Geometry, New Haven, CT, August 17, 2004. |
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Exponential Explorations: Inspiring Students With Their Own Contributions to Number Theory, Joint Meeting of the Mathematical Association of Two-Year Colleges in Connecticut and the Northeast Section of the Mathematical Association of America, Danielson, CT, May 5, 2000. |
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A sample of original compositions. Styles include Jazz, Brazilian, Pop, and Fractal. |
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Fractal music CD in honor of Benoit Mandelbrot for ScienceWriters2010, hosted at the Yale Peabody Museum for the National Association of Science Writers, November 6, 2010.
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A selection of fractal music examples that illustrate specific power-law relations. |
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Jazz guitar performance with 12 piece Latin band Sonido Unidad. |
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"Log-a-Rhythmic" is a futuristic, yet timeless, cross-cultural dance groove. It's based on Robert Schneider's non-Pythagorean scales, and uses an original algorithm to map harmonic and rhythmic structure to prime numbers. |
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"100 Seconds of Pi" is an animation generated from the original algorithmic composition of the same name. All pitches, durations, and dynamics in each of the six voices of the composition are derived from the digits of pi. |
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"Brecker 8," a fractal music composition with accompanying video by Teja Krasek, featured on IBM's website. (See selection number 6 in the section entitled "Fractals in culture and society.") |
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iKandl Birthday App, an eco-friendly, interactive, multimedia greeting app for the iPhone and iPad, now at the iTunes Store. |
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Mandelbrot Zoom, a fractal animation produced for the feature length documentary BACH & friends, January, 2010. |
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The Bach Project interview with filmmaker Michael Lawrence for feature length documentary on Johann Sebastian Bach's pervasive influence in 21st century music, December 5, 2008. |
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Fractal Music Composer is a Java app that enables you to create original prolation canons. |
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Mandelbrot's World of Fractals, Technical consultant for DVD by Nigel Lesmoir-Gordon, Gordon Films UK, in conjunction with Yale University and the National Science Foundation, December, 2003. |
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Liquid Crystal Glass House, Cellular automata programming for Michael Silver's design and exhibit at "Super-ficial: The Surfaces of Architecture in a Digital Age," New Museum of Contemporary Art, Zenith Media Lounge, New York City, January 31 - April 6, 2003. |
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