S T A T E M E N T: "Butterfly Primes ... ~Prejudicial Numbers~ ... ~metamorphosis~"

I have had a fascination with the visual patterns that numbers often make in various scenarios. In the process of looking at that most famous of classical Newtonian physics laws ... the panoramic "Inverse Square Law" ... in its most basic presentation, that is, in a simple multiplication table in which the simple squaring of similar sequential numbers from each axis generates the central diagonal line, the diagonal line of squares ... I became curious as to how those mysteriously alluring and uncontrollable prime numbers might fit in. Surely, their squares, too, had some untold secrets.

Finding that the differences in the squares of any and all primes was always a multiple of 24 was enough to generate some sleepless nights. Digging deeper and finding that specific sets of complementary 24 multiples acted to actually shepherd the prime squares along the diagonal squares line was just short of unbelievable. Surely I was wrong. Many hours over many weeks of testing though seemed to confirm that I had found a pattern for the primes. Not only that, but the pattern, when all the accompanying 24 multiples were included, presented as that lovely of all living forms, flitting here and there ... the butterfly. The "Butterfly Primes" were born.

Now, while the concept in the formation of the "Butterfly Primes" pattern is not overly technical from a descriptive point of view, it really did not answer the question that the pattern begs ... why 24 and what does 24 have to do with the primes on a numerical level?

It was while I was in the middle of the little Q-&-A dialog about prejudicial numbers, and our attitudes and expectations about them, that this very question came to press on me in a relentless fashion. What would the difference in the squares of all numbers (specifically the odds) divided by 24 tell us. What followed was "The Butterfly Prime Directive ... ~metamorphosis". The answer to the number prejudices of the prime was to see how all the numbers played out ... given the same and equal opportunity ... to express their own private specialness. Indeed, what is found was as old as the hills ... as old as the numbers themselves: Numbers don't lie. They don't cheat and they don't even call others names. People do.

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Born in the San Francisco Bay Area and raised in Southern California, Reginald Brooks graduated from Oregon State University with a degree in general science in 1970. Before fully completing a MS degree in cell biology, he moved his young family to Portland to obtain a degree in Medical Technology. After five invigorating years as a medical research specialist he returned to his true love... the visual arts. Thus began a long career as a painter and sculptor with a strong interest in realizing and expressing the amazing world that we inhabit... with a considerable interest in seeing the world without borders...without the overt distinction between the aesthetic, interpretive view of the visual arts and the seemingly plain, yet nevertheless interpretive view of science. Writings on mathematics and physics, both his own and others, have formed the underpinnings of much of his work over the years. New media net.art... work created on and designed to be experience on a computer... has been a new and very exciting part of his output since 2001. This medium has provided a natural collaborative venue for separate media (white papers, prints, drawings, paintings, sculpture and animations) to come together to present a more complete immersive experience to a global audience. He has exhibited his paintings and sculptures in a number of solo (Portland) and group shows across the country.

Writings based on visual art, math, music and physics

  • "LightspeedST: 1. 20 Questions" Part 1 of the 5-part series. Twenty plus question examining the fundamental nature of SpaceTime (ST) and the role the constant "the speed of light" plays. Is there a connection?

  • "LightspeedST: 2. 20 Answers" Part 2 of the 5-part series. Twenty plus answers to the 20+ questions, framed in bite-sized chunks...the better to swallow and digest these tender new morsels. Lightspeed=ST suggests a new view of our Universe(s).

  • "LightspeedST: 3. The Mechanics of SpaceTime (ST) ~A Portrait of SpaceTime~" Part 3 of the 5-part series. Actually, this "Portrait of SpaceTime" was written first. (Actually...really...this is all based on L.U.F.E., the Layman's Unified Field Expose´ from 1985. See Links.) The goal: in the most concise and succinct manner...and always with an eye on simplification...lay out the case for tying together the quantum nature of light with the gravitational dependence of spacetime. LightspeedST Parts 1,2,4,and 5 quickly followed as the antidote.

  • "LightspeedST: 4. The Movie Script" Part 4 of the 5-part series. All text and no play doesn't mean anything more than the notion that every one's individual imagination will play out differently...because that is a good thing! And yet, there is something especially apropos about seeing the original intent...the roadmap to infinity. Don't miss this one! (IN PRODUCTION)

  • "LightspeedST: 5. The Movie" Part 5 of the 5-part series. As a visual journey, "LightspeedST: 5. The Movie" will quickly swoosh you...through moving images and text...up and over, down and through, the highlights of LightspeedST...leapfrogging @ the speed of light. (IN PRODUCTION)

  • "LightspeedST: Links & References" A quick References and Links page.

  • "AFPOP: A Fresh Piece of Pi(e)...and the √2, too...Fractal - Fractal - Fractal"
    "Circles and squares...as well as other geometric forms...have always been inter-related. Inherent in their geometry is the relationship of their linear elements to their areas...forming the basis of the Inverse Square Law (ISL), as formally presented in the Brooks Base Square (BBS) matrix. At their core, these geometric forms are based on three irrational, infinity-based numbers of proportion...π, √2 and φ...pi, the square root of two, and the golden mean. These core proportion-based relationships suggest that they may be acting as fractals in the formation of The Architecture Of SpaceTime (TAOST). Fractals of infinity.!"

  • "GoMAC: The Geometry of Music And Color, Parts II and III." How the natural, geometric divisions of the musical monochord and the color spectrum are inherently derived from the same universal law that informs how light, sound, electromagnetism, gravity...indeed, "The Architecture of SpaceTime" itself...behaves. That law is the Inverse Square Law (ISL) and it has a specific relationship to all the quantitative, whole integer numbers as shown in the Brooks (Base) Square matrix (BBS). Part II of the three-part Geometry of Music And Art (GoMAC) series focuses on a visual journey of how the musical spectrum...and specifically the chromatic and diatonic scales...is based on the ISL. A visual walk-through and summary of key concepts relating the ISL-derived Brooks (Base) Square, BBS, matrix with a geometrically derived division of both the musical monochord...resulting in the chromatic and diatonic major scale...and the color spectrum (as seen in GoMAC part III). Modulations around the Circle of Fifths and the Golden Rectangle are...key. Based on "The Geometry of Music, Art and Structure...linking science, art and esthetics" white paper, "Geometry of Music And Color, I" new media net.art project, and the BBS matrix. Original soundtracks (A and B). Part III focuses on a visual journey of how the color spectrum...and specifically the complementary colors of each hue, is based on the ISL. A visual walk-through and summary of key concepts relating the ISL-derived Brooks (Base) Square, BBS, matrix with a geometrically derived division of both the musical monochord...resulting in the chromatic and diatonic major scale (part II)...and the color spectrum, in which color complements inside and outside of the 400-750 nm visible spectrum dictate the colors that we perceive.

  • "Numbers of Inevitability ~Let’s do a number on that!~" Number relationships are like the best and worst...the highest highs, lowest lows...of the most significant human relationships you have ever known. When they are really wrong it really shows and pretty much everyone can see it. And, when they are right...really right...they seem, well, almost inevitable.

  • "The Architecture Of SpaceTime (TAOST) as defined by the Brooks (Base) Square matrix and the Inverse Square Law (ISL)"
    "The single most important concept to take from here is that not only is ST not rigid and static...indeed it is more like a fluid made of light, each quanta of which flashes on and off...pulse-propagates into and out of existence...at a frequency (and wavelength) according to its energy...and this fluid light ST unit resonates off a wave of energy at the peak of each pulse-flash...that wave, like a pond ripple, fans out to infinity (or the edge of the Universe...which ever comes first) where it is absorbed back into the sub-Planck event horizon (Singularity) to fuel the next round...communicating...passing on information...as to the location source and energy density...the amount and degree of its presence...its curvature...to every other ST unit throughout the Universe(s), BUT that the ST formation and curvature information propagation is informed, dictated and quantified by the matrix of BBS and the ISL...the bean counters par excellence!"

  • "Brooks (Base) Square interactive (BBSi) matrix: Part I: BASICS" ~ This "BASIC" introduction to the matrix grid and the simplest, most fundamental pattern of the numbers that are formed from the main, Prime Diagonal are presented in a step by step fashion in five different interactive, multimedia formats. The Prime Diagonal is none other than square of the axial numbers (1,2,3,...) forming the core of the Inverse Square Law sequence (1,4, 9,...). All the numbers...and their many exquisite patterns...are derived directly from the Prime Diagonal numbers. This is Part I. Part II will follow and will present some of the more interesting patterns. The Inverse Square Law defines how a force or influence (like energy or light) falls off in strength as the distance is increased. It is one of the fundamental relationship laws of the universe effecting everything from gravity to electromagnetism. It can not but help to also be part of the spacetime fabric. It's part of "The Architecture Of SpaceTime" (TAOST).

  • "Brooks (Base) Square (BS): The Architecture of Space-Time (TAOST) and The Conspicuous Absence of Primes (TCAOP) - the complete work (Rules 1-177)"

  • "Brooks (Base) Square (BS): The Architecture of Space-Time (TAOST) and The Conspicuous Absence of Primes (TCAOP) - a brief introduction to the series"
    The table of numbers that, while excluding the *prime numbers ... and only the *prime numbers ... reveals the number patterns that are primary ... primordial ... to the structure of the Universe. This primordial matrix defines the Inverse Square Law (ISL) that informs gravity, light (electromagnetism) and atomic structure ... the underpinnings of that which we see as the observable Universe. It is the architecture of space-time itself ... that which ultimately informs ... that is, reveals its disposition that in turn presents the physical laws, and their expression, of light, gravity and the structure of matter ... that fundamentally defines the true structure of the Universe ... seen and unseen ... encompassing all matter (light and dark) and all energy (light and dark). The ISL is a key relationship describing the interplay of space and time. It is postulated here that the true underpinnings of space-time itself are inherently defined by numerical relationships ... numbers ... the numbers of Brooks (Base) Square (BBS).

  • "GoMAS: The Geometry of Music, Art and Structure ...linking science, art and esthetics" ~ That simple geometric principles can be responsible for the manifestation of the multitudes of beauty, diversity and richness of Nature is further supported here in this paper. The Inverse-Square-Law (ISL), a simple geometric principle, is shown to be the common link between physics, chemistry, biology, and the science and esthetics of music and art. Nature has incorporated the ISL as the major game rule to building the cosmos. Our perception of pleasing form, color and sound is prophetically built into our sensory being, our biologic evolution, and our structural past.

  • 2008-
  • "The Conservation of SpaceTime" ~The role of the Higgs, graviton and photon bosons in defining Dark Matter = Dark Energy (the inverse of) in the fractal Universe~

  • "Quantum Gravity ...by the book" ~merging Quantum Mechanics with Gravity

  • "The History of the Universe - update - 'The Big Void'" ~A short, update supplement to "Dark Matter = Dark Energy (the inverse of): The Conservation of Spacetime by The Conservation of Force" and "The History of the Universe in Scalar Graphics."

  • "The Butterfly Prime Determinant Number Array (DNA) ~conspicuous abstinence~" ~The role of the highly ordered positive space pattern of the odd non-primes in revealing the reverse, negative space pattern of the primes as a determined number array is revealed.
  • "The Butterfly Prime Directive...~metamorphosis~". ~There is a logic behind the ordered and predictable pattern of prime numbers.

  • "Butterfly Primes ... ~let the beauty seep in~". An ordered and predictable pattern for the prime numbers emerges.
  • "The LUFE Matrix: E=mc2...and then some". The focus is on energy. From Einstein's initial insight into the transformation between mass and energy, we now have a large number of similar transformations between energy and the other fundamental parameters of matter...i.e., charge and spin...and their activities within their space-time environments such as velocity and acceleration, frequency and temperature, momentum, pressure and force, potential difference, heat and work, etc. The original Preview-Review Slide Show "Can you say energy 10 different ways?" (see above), included here, is now further enhanced with a showcase of select LUFE Matrix Supplement examples all focused on the various forms that energy can take.

  • "The History of the Universe in Scalar Graphics: (Simultaneous Birth of Black Holes and the Inflationary Universe at the onset of the Big Bang"). A mostly graphical supplement to "Dark Matter = Dark Energy (the inverse of): The Conservation of Spacetime by The Conservation of Force.
  • "The LUFE Matrix: Infinite Dimensions ~a room with a view...within a room with a view...within a room with a view~." A new, speculative journey to account for the multiple dimensions that have informed The LUFE Matrix since its introduction in 1985. FAQ-graphic format.

  • "Dark-Dark-Light: Dark Matter = Dark Energy (the inverse of): The Conservation of Spacetime by The Conservation of Force"
  • "The LUFE Matrix: the distillation of SI units into more fundamentally base units of space and time dimensions" (Short Title: "The Multi-dimensional LUFE Matrix
  • "The LUFE Matrix Supplement: Examples and Proofs"

  • Part II below, from 2000, was rewritten and recast for online publication as a three part series:

  • Part 1: "PIN: Pattern in Number...from primes to DNA" A brief primer on visual patterns found in simple, well known number systems leading into the remarkable number magic and esthetic beauty of the DNA double helix (axial view) found in Part 2."GoDNA"and continued in Part 3."SCoDNA".
  • Part 2: "GoDNA: the Geometry of DNA (axial view) revealed" Which came first? The self replicating underlying geometry or the form itself with its dependence on enzymes, hydrogen bonding and a matching code of bases?
  • Part 3: "SCoDNA: the Structure and Chemistry of DNA (axial view)" Extending "GoDNA" into the realm of structural detail and chemistry forming the composite design.

  • "The Geometry of Music, Art and Structure…linking science, art and esthetics, Part II; self-published. The original material for this paper was presented (self-published) at the 1997 solo exhibition at the Montage Gallery, Portland, OR under the title "Patterns In Numbers: From Prime Numbers to DNA".

  • "The Geometry of Music, Art and Structure…linking science, art and esthetics, Part I presented at the Eighth International Conference on Engineering Computer Graphics and Descriptive Geometry in Austin, TX, sponsored and published by the International Society of Geometry and Graphics. The original material for this was presented at the 1996 solo exhibition at the Montage Gallery, Portland, OR.

  • "The LUFE Matrix: the distillation of SI units into more fundamentally base units of space and time dimension" (Short Title: "The Multi-dimensional LUFE Matrix") with supplement, paper, self-published

  • "Fundamental Constants of Nature: Mass", paper, self-published
  • "Fundamental Constants of Nature: Ratios", paper, self-published
  • "Fundamental Constants of Nature: Charge", paper, self-published
  • "Fundamental Constants of Nature: The LUFE Matrix", paper, self-published

  • "Mass Variation in the Electron by Photon Absorption & The Inverse Square Law", paper, self-published
  • "Expose on Music, Color and the Inverse Square Law", paper, self-published

    1985-(Online 2008)
  • "L.U.F.E.: The Layman’s Unified Field Expose" (a visual guide), textbook-manuscript, self-published



1970- BS General Science, Oregon State University
1972- MS Cell Biology-incomplete, OSU
1973- MT(ASCP) Medical Technology, Good Samaritan Hospital & Medical Center,               Portland, OR
1978- Medical Research Specialist, Good Samaritan Hospital & Medical Center,               Portland, OR
present- New Media=digital tools + IT + the internet

Solo Exhibitions

2008- Lara Sydney Framing Gallery, Portland, OR
2007- Urban Wineworks Gallery, Portland, OR
2007- Lara Sydney Framing Gallery, Portland, OR (2-Person Show)
2005- Lara Sydney Framing Gallery, Portland, OR
2001- Lara Sydney Custom Framing Gallery, Portland, OR
1997- Montage Gallery, Portland, OR
1996- American Institute of Architects/ Portland Chapter, Portland, OR
1996- Montage Gallery, Portland, OR
1995- Montage Gallery, Portland, OR
1992- Zero Square Gallery, Portland, OR
1989- Oregon Graduate Center, Hillsboro, OR
1989- Portland Community College, Rock Creek, OR
1988- Beaverton City Hall, Beaverton, OR
1987- Mt. Hood Community College, Gresham, OR
1987- Beaverton City Hall, Beaverton, OR
1987- Beaverton Chamber of Commerce, Beaverton, OR

Rhizome ArtBase

2012-"AFPOP: A Fresh Piece of Pi(e)...and the √2, too...Fractal - Fractal - Fractal"
2012-"Sunspots and Solar Flares"
2011-"Brooks (Base) Square (BBS) interactive matrix: Basic (Part I)"
2010-"Brooks (Base) Square & The Inverse Square Law (ISL)"
2010-"The Geometry of Music Color"
2006-"Butterfly Primes"
2004-"Your sFace or Mine?"
2003-"Naughty Physics (a.k.a. The LUFE Matrix)
2001-"RealSurReal...aClone, 2001"

Group Exhibitions (select, nonprofit org.)

2012- 30th Annual Visual Arts Showcase 2012, Beaverton Arts Commission, Beaverton, OR
2012- CoCA's Members Show, Seattle Design Center, Seattle, WA
2012- Rhizome ArtBase, http://rhizome.org, "AFPOP: A Fresh Piece of Pi(e)...and the √2, too...Fractal - Fractal - Fractal", New York, NY
2012- Rhizome ArtBase, http://rhizome.org, "Sunspots and Solar Flares", New York, NY
2011- 29th Annual Visual Arts Showcase 2011, Beaverton Arts Commission, Beaverton, OR
2011- Rhizome ArtBase, http://rhizome.org, "Brooks (Base) Square (BBS) interactive matrix: Basic (Part I)", New York, NY
2011- Carkeek Park Outdoor Art Exhibit, "Heaven and Earth 3: Cycles of Return",
         COCA, Seattle, WA
2011- Maude Kerns Art Center, "Oregon Made For Interiors", Eugene, OR
2010- Rhizome ArtBase, http://rhizome.org, "Brooks (Base) Square & The Inverse
        Square Law (ISL)" , New York, NY
2010- Rhizome ArtBase, http://rhizome.org, "The Geometry of Music Color", New
        York, NY
2009- Netart Features 2009, JavaMuseum, Cologne, Germany
2009- 27th Annual Visual Arts Showcase 2009, Beaverton Arts Commission,
          Beaverton, OR
2008- 26th Annual Visual Arts Showcase 2008, Beaverton Arts Commission, Beaverton, OR
2008- "Hollywould", 2008 Freewaves 11th Festival of Experimental Media Art,
          Hollywood, CA
2008- "Welcome the Rain Sculpture Contest", 1st Place Winner, East Multnomah
          County Soil & Water Conservation District, Portland, OR
2008- All-Oregon Art Annual, Professional, juried, Oregon State Fair, Salem, OR
2007- 11th Int'l Conference on Information Visualization (IV07), July 3-7,
           Swiss Federal Institute of Technology, Zurich, Switzerland, DART gallery
2007- 4th Int'l Conference Computer Graphics, Imaging and Visualization (CGIV07),
           August 14-17, KMUTT, Bangkok, Thailand, DART gallery
2007- "Pacific Northwest Art Annual 2007", Cultural Forum, U. of Oregon, Eugene, OR
2007- 2006[10th] Japan Media Arts Festival, Tokyo Metropolitan Museum of
           Photography, Feb 24-Mar4, 2007
2007- "Allegories of the Genome", Vancouver, BC, Canada-online gallery-
2006- Rhizome ArtBase, http://rhizome.org, "Butterfly Primes...Prejudicial Numbers", New York, NY
2006- 10th Int'l Conference on Information Visualization (IV06), July 4-7,
           University of London, London, England, DART gallery
2006- Int'l Conference Computer Graphics, Imaging and Visualization (CGIV06),
           July 25-28, Sydney, Australia, DART gallery
2006- "ARTIFICIAL A.GENDER? new media online exhibition:tba
2004- Eurographics 2004, Art Show "Art and Science", Grenoble, France, 30 Aug -
           3 September, 2004
2004- Rhizome ArtBase, http://rhizome.org, "Your sFace or Mine?", NY, NY
2004- "21 Years of Studios", Cathedral Park Place (invitational), Portland, OR
2003- Rhizome ArtBase, http://rhizome.org, "naughty physics (a.k.a. The LUFE
          Matrix)", NY, NY
2002- Bellevue Sculpture Exhibition 2002, City of Bellevue, WA
2002- Rhizome ArtBase, http://rhizome.org, "Hey! U funk'n with my DNA?", NY, NY
2002- Net.Art, The Irish Museum of Modern Art,
2002- 20th Annual Visual Arts Showcase 2002, Beaverton Arts Commission,
          Beaverton, OR
2001- Net_Working, net.art, CHArt conference and Watershed Digital Cafe, Bristol,
          UK www.watershed.co.uk/Net_Working
2001- FILE_2001 (Electronic Language International Festival), net.art, Museu da
          Imagem e do Som,Sao Paulo, Brazil, August 7th-September 2nd, 2001.
          Online all year at: http://www.file.org.br
2001- Rhizome ArtBase, http://rhizome.org, "RealSurReal...aClone, 2001", NY, NY
2000- PICA, "Open Walls" (unjuried), Portland, OR
1997- Beaverton Showcase '97, Beaverton Arts Commission, Beaverton, OR
1996- Beaverton Showcase '96, Beaverton Arts Commission, Beaverton, OR
1995- Maude Kerns Art Center, "5th Sculpture Biennial", Eugene, OR
1995- Maude Kerns Art Center, Womenís Art Triennial, Eugene, OR
1994- Beaverton Showcase '94, Beaverton Arts Commission, Beaverton, OR
1993- Maude Kerns Art Center, "The Silent Child, Art as Healing", Eugene, OR
1992- Kinsey Gallery, Seattle University, Seattle, WA
1991- A.I.R. Gallery, "Choice"(unjuried), New York, NY
1989- Maude Kerns Art Center, "Icons and Idols, A Celebration of Ceremony",           Eugene, OR
1989- Justice Center Sidewalk Gallery, Portland, OR
1988- Newport Visual Arts Center, "Nuclear Visions", OCCA, Newport, OR
1988- Beaverton Showcase '88, Beaverton Arts Commission, Beaverton, OR
1988- Annual Juried Art Show, Umpqua Community College, Roseburg, OR
1987- Beaverton Showcase '87, Beaverton Arts Commission, Beaverton, OR
1987- 17th Annual Willamette Valley Exhibition Corvallis Art Center, Corvallis, OR
1986- Northwest Artistís Workshop, "On the Job", Portland, OR
1986- Beaverton Showcase '86, Beaverton Arts Commission, Beaverton, OR
1985- Germanow Art Gallery, "Current Visions ë85", JCC, Rochester, NY
1983- Northwest Artistís Workshop, "Description/ Portrayal" (Invitational), Portland,           OR
1983- PCVA, "Public Hanging" (unjuried), Portland, OR
1983- Arrowmont School of Arts & Crafts, "The Figure: New Form, New Function",
          Gatlinburg, TN
1983- "1st Annual Sherbrooke Intíl Painting Salon", Sherbrooke, Quebec, Canada
1981- PCVA, "Public Hanging" (unjuried), Portland, OR
1978- Northwest Artistís Workshop, "Salon de Refuses" (unjuried), Portland, OR

Past solo show theme titles (Paintings and sculpture):

"~breathe~ A Celebration of Women", 2008
"A Void", 2007
"Infinite Dimensions...without borders", 2005
"The E-P Series: digital-encaustic with scratchboard", 2001
"Dance Number Appendage: A Surrealistic Look At Patterns in Dance and Numbers", 1997
"Lucy:Contemporary Reflections on Paleonathropologic Findings",1996
"A Search for the Multicultural Mythology of Our Times", 1991


"The Geometry of Music, Art and Structure...linking the esthetics of Art and Science" at the 8th ICECGDG (International Conference on Engineering Design Graphics and Descriptive Geometry, sponsored by the International Society for Geometry and Graphics, the Japan Society for Graphic Science, and the Engineering Design Graphics Division of the American Society for Engineering Education; hosted by the College of Engineering, The University of Texas at Austin).1998.
Published in the Proceedings of the 8th ICECGDG, Vol. 2, pg 378, ISGG, Tokyo, Japan, 1998

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