Plus Blog

November 25, 2009
Wednesday, November 25, 2009

An amateur fractal programmer has discovered a new 3D version of the Mandelbrot set. Daniel White's new creation is based on similar mathematics as the original 2D Mandelbrot set, but its infinite intricacy extends into all three dimensions, revealing fractal worlds of amazing complexity and beauty at every level of magnification.



posted by Plus @ 9:45 AM


At 12:56 PM, Anonymous Anonymous said...

I want this as screensaver,awesome

At 2:27 PM, Blogger David Makin said...

Those interested in more about the Mandelbulb and the search for the "true 3D" Mandelbrot including an almost complete history of the last couple of years search may wish to look here

At 10:30 AM, Blogger miner49er said...

What's the explanation for the fracvtal nature of the mandelbrot set? Is it an anomoly in the number system? Is it basically an error?

I have been fascinated by fractals for 20 years but never really thought about _why_ they (mandelbrot/escape-time) exist.

I wonder if discovering why they exist at all, may lead to a 'better' 3D analog?

At 7:06 AM, Blogger Djeimz said...

Interesting article. Interesting pictures.

However, I'm wondering if there isn't a typo in the formula given. If it is a direct generalization of complex multiplication using Euler angles, the z-component should be:
-sin(n phi)
and not:
-sin(n theta)
Am I wrong?


At 10:25 AM, Anonymous The Plus Team said...

Thanks Djeimz, you're right and it's been corrected!

At 12:12 AM, Blogger Paolo Bonzini said...

It is possible to describe this fractal also using quaternions. This is interesting in that it removes the need to define a special, non-standard exponentiation function.

See [PDF] (thanks to the people on and for proofreading!)

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November 19, 2009
Thursday, November 19, 2009

LHC set for restart

After over a year of repair works the Large Hadron Collider at CERN may be restarted within the next few days. Scientists will gently prod the giant particle collider back into action, starting by circulating beams of protons at low energies and generating low energy collisions, before slowly firing it up to its full power. It is hoped that eventually the high energy collisions will generate conditions similar to those right after the Big Bang and shed light on some of the biggest mysteries of the Universe.

To remind yourself of what the LHC is all about, read the Plus articles:

Or, for a quick fix, here's the LHC rap:

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November 18, 2009
Wednesday, November 18, 2009

Happy 150th birthday to the Riemann Hypothesis - the most famous unsolved problem in mathematics

It has been 150 years since the mathematician Bernhard Riemann published the conjecture which is now one of the most important unsolved problems in mathematics. The Riemann hypothesis encapsulates humankind's attempt to understand the mysteries of the primes: why there is no apparent pattern in the way the primes are distributed on the number line. The hypothesis is one of the Clay Mathematics Institute's Millennium Prize Problems — anyone who proves (or disproves) it will receive one million dollars.

If you'd like to have a go at solving the Riemann hypothesis yourself, then learn more about it in the Plus articles A whirlpool of numbers, The prime number lottery, and The music of the primes. To find out more about the Clay Institute Millennium Prize Problems, read How maths can make you rich and famous, Part I and Part II.

posted by Plus @ 11:38 AM


At 4:26 AM, Blogger westius said...

you'll like this cartoon from

I just finished reading 'The Music of the Primes' - great book, would highly recommend it.

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November 12, 2009
Thursday, November 12, 2009

What are the chances of winning the lottery? How much of a football team's league position is due to luck and how much is due to skill? What are the chances of a false positive test result in security or medical screening? Which newspaper headlines are telling the truth? Can you spot a scam before you fall for it?

Probability and statistics help to provide answers to questions like these, but they are often misunderstood. The Millennium Mathematics Project (the home of Plus) and Winton Programme for the Public Understanding of Risk are addressing this with a new schools outreach project entitled What are the Odds? The Hands-On Risk and Probability Show...



posted by Plus @ 1:02 PM


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November 12, 2009
Thursday, November 12, 2009

Maths in a minute - combinatorics

And while we're on the topic of probability, let's answer one of those important mathematical question: how likely are you to win the lottery?

In the UK lottery you have to choose 6 numbers out of 49, and for a chance at the jackpot you need all of your 6 numbers to come up in the main draw. So the question is really how many possible combinations of 6 numbers can be drawn out of 49? There are 49 possibilities for the first number, 48 for the second, and so on to 44 possibilities for the sixth number, so there are 49 x 48 x 47 x 46 x 45 x 44 = 10068347520 ways of choosing those six numbers... in that order. But we don't care which order our numbers are picked, and the number of different ways of picking 6 numbers are 6 x 5 x 4 x 3 x 2 x 1 = 6! = 720. Therefore our six numbers are one of 49 x 48 x 47 x 46 x 45 x 44 / 6! = 13983816 so we have about a one in 14 million chance of hitting the jackpot. Hmmm...

But on a brighter note, we have just discovered a very useful mathematical fact: the number of combinations of size k (sets of objects in which order doesn't matter) from a larger set of size n is n! / (n-k)! / k!.

This sort of argument lies at the heart of combinatorics, the mathematics of counting. It might not help you win lotto, but it might keep you healthy. It is used to understand how viruses such as influenza reproduce and mutate, by assessing the chances of creating viable viruses from random recombination of genetic segments.

You can read more on combinatorics, including money (lotto), love (well kissing frogs) and fun (juggling and rubiks cubes) on Plus.

posted by Plus @ 1:18 PM


November 6, 2009
Friday, November 06, 2009

Maths Inspiration event in Cambridge — November 24th

There are still places left at the Maths Inspiration morning event in Cambridge on 24th November, organised by Rob Eastaway. All Maths Inspiration events are aimed at sixth formers and more able Year 11 students.

The Cambridge events will be held in West Road Concert Hall on 24th November 2009, 9.45am - 12.30, repeated 1pm - 3.45pm. Speakers include Claire Ellis, Professor Chris Budd, Dr Hugh Hunt and Professor David Spiegelhalter, with talks including What have mathematicians ever done for us?, The Maths of breakfast, and The subtle science of uncertainty.

Tickets are £6 per attendee at all events with one teacher entitled to free entry for every ten students.

For full details of all events and to book tickets, please see the Maths Inspiration website, or contact

posted by Plus @ 2:24 PM


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