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Harlan Brothers

Featured Book

Benoit Mandelbrot: A Life in Many Dimensions

Benoit Mandelbrot: A Life in Many Dimensions

A marvelous collection of articles, many by those who worked with Benoit, memorializing the remarkable breadth and depth of his work in science & art.

2014

Michael Frame, et al.

Michael Frame, Nathan Cohen

Stories

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Pascal’s Prism

First published in 2012, this 3-dimensional extension of Pascal’s triangle is a wonderland of significant number sequences

8 min read2 days ago

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Pascal’s Prism

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The Ultimate Guide to Recamán’s Sequence

Subtract if you can, add if you can’t — a simple rule leads to wild behavior and musical structure

8 min readJun 10, 2024

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The Ultimate Guide to Recamán’s Sequence

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Pascal’s Triangle and Powers of e

The base of the natural logarithm is deeply woven through Pascal’s triangle — in an infinite number of ways!

6 min readMay 31, 2024

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Pascal’s Triangle and Powers of e

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The Unlikely Existence of The Cosmological Theorem

Audioactive sequences and the playful genius of John Conway

8 min readMay 13, 2024

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The Unlikely Existence of The Cosmological Theorem

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If Escher Made Music

Psychoacoustics, Shepard tones, and the logarithmic perception of pitch

5 min readApr 1, 2024

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If Escher Made Music

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Cantor’s Paradise

The Brilliance of Lewis Fry Richardson

A polymath and visionary, Richardson was driven by his concern for humanity

7 min readMay 22, 2024

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The Brilliance of Lewis Fry Richardson

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Cantor’s Paradise

Seeing the Invisible

Abraham Wald and the power of the mind’s eye

5 min readMay 1, 2024

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Seeing the Invisible

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Cantor’s Paradise

St. Elmo’s Fire

This mesmerizing spectacle of nature has been considered both a good omen and a harbinger of danger. The underlying physics help explain…

6 min readApr 23, 2024

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St. Elmo’s Fire

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Harlan Brothers
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Researchers Discover a Fractal Protein

Amazingly, cyanobacterium Synechococcus elongatus spontaneously forms Sierpinski triangles

5 min readApr 16, 2024

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Researchers Discover a Fractal Protein

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Cantor’s Paradise

A Solution to the Problem of Deepfakes

Public key encryption holds an answer to the ever-expanding epidemic of disinformation and outright fakery

7 min readApr 8, 2024

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A realistic-looking, AI-generated image of Jlo (Jennifer Lopez) leaning against Albert Einstein from behind. They look casual and relaxed as if they are on vacation.

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Harlan Brothers

Harlan Brothers

Book Author

Researcher | Mathematician | Composer | Educator | Inventor | Editor for Cantor's Paradise www.harlanjbrothers.com

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