How Mandelbrot’s fractals changed the world

Did you know that the whole universe is fractal?

I think that this article written by Jack Challoner will stir your imagination about he magical nature of fractals.

Challoner writes for BBC online news magazine


“In 1975, a new word came into use, when a maverick mathematician made an important discovery. So what are fractals? And why are they important?

During the 1980s, people became familiar with fractals through those weird, colourful patterns made by computers.

But few realise how the idea of fractals has revolutionised our understanding of the world, and how many fractal-based systems we depend upon.

On 14 October 2010, the genius who coined the word – Polish-born mathematician Benoit Mandelbrot – died, aged 85, from cancer.

Unfortunately, there is no definition of fractals that is both simple and accurate. Like so many things in modern science and mathematics, discussions of “fractal geometry” can quickly go over the heads of the non-mathematically-minded. This is a real shame, because there is profound beauty and power in the idea of fractals.

The best way to get a feeling for what fractals are is to consider some examples. Clouds, mountains, coastlines, cauliflowers and ferns are all natural fractals. These shapes have something in common – something intuitive, accessible and aesthetic.

They are all complicated and irregular: the sort of shape that mathematicians used to shy away from in favour of regular ones, like spheres, which they could tame with equations.

Mandelbrot famously wrote: “Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.”

The chaos and irregularity of the world – Mandelbrot referred to it as “roughness” – is something to be celebrated. It would be a shame if clouds really were spheres, and mountains cones.

Look closely at a fractal, and you will find that the complexity is still present at a smaller scale. A small cloud is strikingly similar to the whole thing. A pine tree is composed of branches that are composed of branches – which in turn are composed of branches.

A tiny sand dune or a puddle in a mountain track have the same shapes as a huge sand dune and a lake in a mountain gully. This “self-similarity” at different scales is a defining characteristic of fractals.

The fractal mathematics Mandelbrot pioneered, together with the related field of chaos theory, lifts the veil on the hidden beauty of the world. It inspired scientists in many disciplines – including cosmology, medicine, engineering and genetics – and artists and musicians, too.

The whole universe is fractal, and so there is something joyfully quintessential about Mandelbrot’s insights.

Fractal mathematics has many practical uses, too – for example, in producing stunning and realistic computer graphics, in computer file compression systems, in the architecture of the networks that make up the internet and even in diagnosing some diseases.

Fractal geometry can also provide a way to understand complexity in “systems” as well as just in shapes. The timing and sizes of earthquakes and the variation in a person’s heartbeat and the prevalence of diseases are just three cases in which fractal geometry can describe the unpredictable.

Another is in the financial markets, where Mandelbrot first gained insight into the mathematics of complexity while working as a researcher for IBM during the 1960s.

Mandelbrot tried using fractal mathematics to describe the market – in terms of profits and losses traders made over time, and found it worked well.

In 2005, Mandelbrot turned again to the mathematics of the financial market, warning in his book The (Mis)Behaviour of Markets against the huge risks being taken by traders – who, he claimed, tend to act as if the market is inherently predictable, and immune to large swings.

Fractal mathematics cannot be used to predict the big events in chaotic systems – but it can tell us that such events will happen.

As such, it reminds us that the world is complex – and delightfully unpredictable.

More of Jack Challoner’s writings can be found at Explaining Science

A biography of Benoit Mandelbrot can be found here

Main stream science is dominantly event-orientated

Is this why main stream science seems to have some of the difficulties it does?

Event oriented thinking sees the world as a complex succession of events rather than as a system as a whole. An event is behavior that happened or will happen. Event oriented thinking assumes that each event has a cause and that changing the cause will correspondingly change the event. The rest of the system that produced the event need not be considered.


Structural thinking sees the world as a complex structure composed of nodes, relationships, and interacting feedback loops. Once the structure is modeled, simulated and understood the fundamental behavior of the system becomes plainly obvious, making the system’s response to solution efforts predictable.

The central tenant of structural thinking is that the behavior of a complex system cannot be correctly understood without thoughtful construction of a model of the key structure of the system, and computer simulation of that model.

Ideas quoted from subsections of:

The Future of Fundamental Physics

It is important that you view the contents of this blog in relationship to my new blog entitled: “The fundamental universe revisited“. This new blog is designed to be the master science referential blog for all my science blog postings in my website.

I share with my readers the ideas about physics of this distinguished theoretical physicist Nima Arkani-Hamed

The principle text can be found in this pdf file. I have extracted the quotes below from this paper in order to provide you with a guide to what the principle themes Nima Arkani-Hamed is promoting. The text speaks for itself.



Fundamental physics began the twentieth century with the twin revolutions of relativity and quantum mechanics, and much of the second half of the century was devoted to the construction of a theoretical structure unifying these radical ideas. But this foundation has also led us to a number of paradoxes in our understanding of nature. Attempts to make sense of quantum mechanics and gravity at the smallest distance scales lead inexorably to the conclusion that space-time is an approximate notion that must emerge from more primitive building blocks. Furthermore, violent short-distance quantum fluctuations in the vacuum seem to make the existence of a macroscopic world wildly implausible, and yet we live comfortably in a huge universe. What, if anything, tames these fluctuations? Why is there a macroscopic universe? These are two of the central theoretical challenges of fundamental physics in the twenty-first century. In this essay, I describe the circle of ideas surrounding these questions, as well as some of the theoretical and experimental fronts on which they are being attacked…”

“…But there is a deeper reason to suspect that something much more interesting and subtle than “atoms of space-time” is at play. The problems with space-time are not only localised to small distances; in a precise sense, “inside” regions of space-time cannot appear in any fundamental description of physics at all…”

“…The fact that quantum mechanics makes it impossible to determine precisely the position and velocity of a baseball is also irrelevant to a baseball player. However, it is of fundamental importance to physics that we cannot speak precisely of position and momentum, but only position or momentum…”

“…This simple observation has huge implications. As discussed above, precise observables require a separation of the world into a) an infinitely large measuring apparatus and b) the system being studied…”

“…It should be clear that we have arrived at a bifurcatory moment in the history of fundamental physics, a moment that has enormous implications for the future of the subject. With many theoretical speculations pointing in radically different directions, it is now up to experiment to render its verdict!…”

“…Today, however, we confront even deeper mysteries, such as coming to grips with emergent time and the application of quantum mechanics to the entire universe. These challenges call for a bigger shift in perspective. Is there any hope for taking such large steps without direct input from experiment?…” [Emergent time relates to the concept of ‘NOW’ and its associated simultaneity].

“…Why should it be possible to talk about Newton’s laws in such a different way, which seems to hide their most essential feature of deterministic evolution in time? [Which I agree with] We now know the deep answer to this question is that the world is quantum-mechanical…”

“…There must be a new way of thinking about quantum field theories, in which space-time locality is not the star of the show and these remarkable hidden structures are made manifest. Finding this reformulation might be analogous to discovering the least-action formulation of classical physics; by removing space-time from its primary place in our description of standard physics, we may be in a better position to make the leap to the next theory, where space-time finally ceases to exist…”

Also see my blog entitled “The emerging crisis in physics. Will physics soon need to take a new course of direction?

An important and sad story about the famous Voyager space probes

Whilst it seems that the lifespan of the to Voyager probes may span out to 2030 the missions themselves are presently being wound down

An important part of the reason for this is that the administrators of the program are nearing the end of their working lives. This New York Times Magazine article also states that these aged administrators are the only people capable of handling the antiquated technology of the Voyager probes.

I quote from the New York Times Magazine article:

“As the Voyager mission is winding down, so, too, are the careers of the aging explorers who expanded our sense of home in the galaxy… …For the foreseeable future, Voyager seems destined to remain in the running for the title of Mankind’s Greatest Journey, which might just make its nine flight-team engineers — most of whom have been with the mission since the Reagan administration — our greatest living explorers. They also may be the last people left on the planet who can operate the spacecraft’s onboard computers, which have 235,000 times less memory and 175,000 times less speed than a 16-gigabyte smartphone. And while it’s true that these pioneers haven’t gone anywhere themselves, they are arguably every bit as dauntless as more celebrated predecessors.”

Essays written by scientists

1.1 This highly important physics paper is suggesting that consciousness is outside of us and if this is the case this has military implications as well. My belief is that our personal consciousness is not outside of us but that our personal (implicit) awareness is. In this sense I believe the ideas of this author.

1.2 Ecosystem Services and Beyond: Using Multiple Metaphors to Understand Human Environment Relationships

1.3 Non-commutative Geometry, the Bohm Interpretation and the Mind-Matter Relationship


1.4 When Reality is Real: An Interview with Antony Valentini

1.5 Some Personal Reflections on Quantum Non-locality and the Contributions of John Bell

Personal Reflections on Quantum Non-locality and the Contributions

1.6 Process, Distinction, Groupoids and Clifford Algebras: an Alternative View of the Quantum Formalism. [Note certain items in pages 1 to 6 of this pdf file have been loosely embraced in my work]

Clifford algebra Basil Hiley.pdf

Did you know that there is at least 18 different interpretations of Quantum Mechanics?

It is important that you view the contents of this blog in relationship to my new blog entitled: “The fundamental universe revisited“. This new blog is designed to be the master science referential blog for all my science blog postings in my website.

I think that it is important for my readers to appreciate the significance of the contents of this blog

In my science writings I attempt to keep in mind the de Broglie-Bohm model of quantum theory. You will find this theory in listed on pages 3-4 of the pdf document below.

Eighteen interpretations of QM.pdf

Quarks and creation

‘Perfect’ Liquid Hot Enough to be Quark Soup; Protons, neutrons melt to produce ‘quark-gluon plasma’ at RHIC

This seems to be an amazing story about scientists having created a new form of matter.


“This research offers significant insight into the fundamental structure of matter and the early universe, highlighting the merits of long-term investment in large-scale, basic research programs at our national laboratories,” said Dr. William F. Brinkman, Director of the DOE Office of Science. “I commend the careful approach RHIC scientists have used to gather detailed evidence for their claim of creating a truly remarkable new form of matter.”

Non-commutative Geometry, the Bohm Interpretation and the Mind-Matter Relationship

I introduce you to an esteemed mathematician who talks about this intriguing subject


It is argued that in order to address the mind/matter relationship, we will have to
radically  change  the  conceptual  structure  normally  assumed  in  physics.    Rather
than  fields  and/or  particles-in-interaction  described  in  the  traditional  Cartesian
order  based  a  local  evolution  in  spacetime,  we  need  to  introduce  a  more  general
notion of process described by a non-commutative algebra.  This will have radical
implications  for  both  for  physical  processes  and  for  geometry.  By  showing  how
the  Bohm  interpretation  of  quantum  mechanics  can  be  understood  within  a  non-
commutative structure, we can give a much clearer meaning to the implicate order
introduced by Bohm.  It is through this implicate order that mind and matter can
be seen as different aspects of the same general process.