Blog Archives

What If You Dig A Hole Through The Earth?

April 26, 2014
By
What If You Dig A Hole Through The Earth?

It suddenly struck me that that tiny pea, pretty and blue, was the Earth. I put up my thumb and shut one eye, and my thumb blotted out the planet Earth. I didn’t feel like a giant. I felt very, very small (Neil Armstrong) Where would you come out if you dig a hole straight

Read more »

The Pythagorean Tree Is In Bloom

April 9, 2014
By
The Pythagorean Tree Is In Bloom

There is geometry in the humming of the strings, there is music in the spacing of the spheres (Pythagoras) Spring is here and I will be on holiday next week. I cannot be more happy! It is time to celebrate so I have drawn another fractal. It is called the Pythagorean Tree: Here you have

Read more »

The Collatz Fractal

April 4, 2014
By
The Collatz Fractal

It seems to me that the poet has only to perceive that which others do not perceive, to look deeper than others look. And the mathematician must do the same thing (Sofia Kovalevskaya) How beautiful is this fractal! In previous posts I colored plots using module of complex numbers generated after some iterations. In this

Read more »

Do Not Play With Mr. Penney

April 1, 2014
By
Do Not Play With Mr. Penney

Facts do not speak (Henry Poincare) Mr. Penney is my best friend. He is maths teacher and loves playing. Yesterday we were in his office at the university when he suggested me a game: When you toss a coin three times, you can obtain eight different sequences of tails and heads: TTT, TTH, THT, HTT, THH,

Read more »

Blurry Fractals

March 27, 2014
By
Blurry Fractals

Beauty is the first test; there is no permanent place in the world for ugly mathematics (G. H. Hardy) Newton basin fractals are the result of iterating Newton’s method to find roots of a polynomial over the complex plane. It maybe sound a bit complicated but is actually quite simple to understand. Those who would

Read more »

Random Love

March 23, 2014
By
Random Love

Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin (John von Newman) Ms. Positive and Mr. Negative live in a one-dimensional world and are falling in love. But beginnings are not always easy. They have a big problem: none of them like the other’s neighborhood. Ms. Positive

Read more »

The Lonely Acacia Is Rocked By The Wind Of The African Night

March 13, 2014
By
The Lonely Acacia Is Rocked By The Wind Of The African Night

If you can walk you can dance. If you can talk you can sing (Zimbabwe Proverb) There are two things in this picture I would like to emphasise. First one is that everything is made using points and lines. The moon is an enormous point, stars are three small nested points and the tree is

Read more »

Dora’s Choice

March 9, 2014
By
Dora’s Choice

Arithmetic is being able to count up to twenty without taking off your shoes (Mickey Mouse) On her last mission, Dora The Explorer sails down the Amazon river to save her friend Isa The Iguana from Swiper The Fox claws. After some hours of navigation, Dora sees how the river divides into 3 branches and

Read more »

Warholing Grace With Clara

March 3, 2014
By
Warholing Grace With Clara

Do not believe anything: what artists really do is to hang around all day (Paco de Lucia) Andy Warhol was mathematician. At least, he knew how clustering algorithms work. I am pretty sure of this after doing this experiment.  First of all, let me introduce you to the breathtaking Grace Kelly: In my previous post

Read more »

Face To Face With Marilyn Monroe

February 24, 2014
By
Face To Face With Marilyn Monroe

Symmetry is what we see at a glance (Blaise Pascal) Ladies and gentlement, the beautiful Marilyn Monroe: There are several image processing packages in R. In this experiment I used biOps, which turns images into 3D matrices. The third dimension is a 3-array corresponding to (r, g, b) color of pixel defined by two other

Read more »