Rethinking Randomness by Jeff Buzen

RR1 RR2Rethinking Randomness by Jeff Buzen introduces an alternative characterization of randomness and a new modeling framework that together explain the improbable success of these probabilistic models. Jeff used one of my close packing circle arrangements with a corresponding line lattice (connecting circle contacting points) and then an apparently random image selection (cover design) conjured by the line lattice – as a sort of analogy of his concept. Jeff’s book is a good read for those working probabilistic models.

 

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Crystal Cave – A new book of geometric designs to color

This is a new book that has just gone to print for Wooden Books (UK) and Bloomsbury (USA, Australia, India). Title is the “Crystal Cave.” The book is full of geometric designs to color by Ensor Holiday, Roger Burrows (me), Roger Penrose, John Martineau, and Haifa Khawaja. Each author has applied different math systems to generate the designs – and all the designs have been selected to stimulate the mind and creativity. Ensor Holiday and I have created designs based on close-packing circles bound by squares and triangles; Roger Penrose designs are based on non-periodic tilings (tiles extracted from regular pentagons); John’s designs are circle based but where circles ‘grow,’ from close packing circle points; Haifa’s designs are classic Islamic designs mostly based on tessellations with some overlap onto systems based on the Islamic ‘Ray,’ method.

Altair Crystal Cave UK

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Think 3D completed

The book has now been completed and will be published by Thames and Hudson Ltd in June 2016 (now Spring 2017).  I’ve constantly updated the work awaiting publication and have included the latest technologies and future applications for the various types of geometry and visual logic featured in the book – particularly the shape changers and the dynamic sphere geometry. Advance proof-copies are available for review. To see why the shape-changer geometries included in Think 3D are so relevant see the following two examples of a whole new wave of applications that will impact almost everything from architecture to aircraft, packaging, and land/space vehicle design:

https://www.youtube.com/watch?v=CihMimZc3Ac

https://www.youtube.com/watch?v=6cdfWdHZRrE

Think 3D contents are:

Introduction

Visual Logic

Old Traditions and New Directions

Perception and Conceptual Models

Development Of Architectural Form

Geometry Through Time

Neolithic Geometries

The River Cultures

The Indus

The Nile

The Yellow and Yangste

The Tigris and Euphrates

The Pythagoreans

European Tribal Geometry

Geometries of Early Islam

The Renaissance

Out of the Past Into the Future

Cartesian Geometries

Fractals

Shape-Changers

Dynamic Circles & Spheres

The Future of 3D Geometry

Conclusion

Index & Credits

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Think 3D – Update

Have completed the new chapters – the Renaissance and the River Valleys (Euphrates, Tigris, Nile, Yellow, Indus). The new material took longer to create than I thought. Have been working through the illustrations and securing rights for photos when needed. After that the index will need to be completed…The final page count will be just about 360 + pages.

Some of the material that appears in the book will be exhibited in an upcoming exhibition at the Leonardo.

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PCCAPS

Have been working with three high school seniors, and one junior, on projects for Rockwell Collins and Overstock.Com – as part of the PCAPS program, Park City, Utah. The CAPS concept is to link students with corporations and have them work on real projects that will build their professional skills, broaden their experience with hardware and software platforms, and push them into situations that need innovation and sheer hard work. The learning curve for some of the software is pretty steep – but the students are doing well. Next semester I’ll have ten students and we have some interesting projects lined up including one for the USAF.

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THINK 3D

The publisher has asked for new chapters and I have been in the process of adding chapters that cover the geometries of the “river cultures,” – Indus Vally; The Nile; The Euphrates; The Yellow River. I have also broadened the Celtic chapter content to include a broader range of European tribal geometries – primitive as they often are. Also a new chapter on the European Renaissance geometries. To develop the new sections and chapters I have had to do lots of research but the new material really helps show how visual concepts have developed over time, how local cultures have impacted concepts, and also how unique many of the concepts were, and still are – and how these unique concepts of the past can be applied in the present and possible future.

The page count will probably end up around 350 bt could reach 400 – full of illustrations, diagrams, designs, and links to animations, and movie clips. Throughout the book I’ve worked hard to be original and within the pages you’ll find many new discoveries and insights. I have printed samples of the book, “working copies still in process,” for review.

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Think 3D – First draft completed as of tonight

I underestimated the number of pages – once the photo credits and links have been added the count will be in the order of 300 pages. The new working title is, “Think 3D” – “A design source book.” Recent drafts have been with Thames and Hudson and my hope is that they will publish the print edition. It looks like I will retain the electronic edition rights – and have completed all of the animations etc., for electronic editions.

The book traces the development of visual logic from Neolithic times through Greek, Celtic, Islamic, and Renaissance cultures – and through to the present and possible future. The intent of the book is not to repeat what is generally known but to reveal new insights and new ideas – with the objective of demonstrating that geometry is something much more than that of popular conception – it is a visual language that must evolve to meet new needs, to utilize new technologies, and to change the way we think about what we observe in the world around us.

The contents are: Introduction; Old Traditions And New Directions; Perception & Conceptual Models; Development Of Architectural Form; Geometry Through Time; Neolithic Geometries; The River Cultures (Nile, Euphrates, Indus Valley, Yellow River); The Pythagoreans; European Tribal Geometries; Geometries of Early Islam; The Renaissance; Shape Changing Polhedra; Dynamic Sphere Geometry; 3D Geometric Cursive Forms; 3D Fractal Forms; The Future; Conclusion; Index, Credits & Links.

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Concepts of Visual Logic Update

Am now on page 214 after an edit. Have added a really simple convergence proof for the Fibonacci ratio converging on Phi – so simple that it could even be Pythagorean. Also added an exact and not a fudged analysis of DaVinci’s  Vitruvian man with no relation to Phi, just Vitruvius.  This is all in the Perspective chapter – an odd place you might think – but it follows nicely after Egyptian grids on the way to perspective drawings, Futurism, Cubism, etc.

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Concepts of Visual Logic

This is the new working title after “Universe of Geometries.” Now on page  200 and  have  continued to add new material to Neolithic, Greek & Pythagorean, Celtic, and Islamic sections. Have more or less completed the Shape Changing Polyhedra section but still have more to add to the Dynamic Close-Packing Sphere section. The latest section is Perspective but have been using it to not only track the development of grids, from Egyptian  through the Renaissance, and the present, but also to address the concept of harmony in architectural design using complete sphere packing geometries; where each detail is  determined by sphere position. Same would apply to some of the other 3D systems. Might add some irregular 3D curved structures too but need to establish a 3D integrated basis rather than just have casual curves. Still aim to complete the first draft by April 30th although, if I included all my work the book could have 1,000 pages. Over 1,t000 original illustrations so far plus photos.

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A Universe Of Geometries

Am now 110 pages into my new book, A Universe Of Geometries,”  with about 200 pages to go. I aim to complete by the end April. The book is content rich, packed with info, and intended as a course, and source, book for architectural and design students, musicians, artists, structural engineers, mathematicians, scientists and those interested in enhancing perception. Am hoping to give guest lectures and run workshops and exhibitions using the book as the foundation. There’s nothing as rich or thorough out there. Final count on the illustrations will be over 1,000 – have drawn them all – plus some photos. Content includes a lot of my geometrical work accumulated over the last 40 years – scary thought that!

“Universe,” contains an analysis of ancient 2D and 3D geometrical systems and includes many new discoveries and perspectives; from Neolithic through Greek, Celtic, and Islamic. The book also contains modern geometries such as Geodesics, and new Cursive – and then my Dynamic Close-Packing Sphere and Geometric Shape Changing geometries (have discovered a second “Golden Ratio” close-packing). The content includes architectural, structural, scientific, and new material applications (nano-materials), as well as analysis of sound properties, light properties, and sensory enhancing properties, including the use of spaces, color, light, sound, symbolism, perception enhancing designs, and usage of structural materials, etc. The book, in a way, follows the traditions, philosophy, and knowledge base, associated with the Pythagoreans but to a much more advanced level.
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