Ford, there is an infinite number of monkeys outside who want to talk to us about this script for Hamlet they have worked out (from Episode 2 of The Hitchhiker’s Guide to the Galaxy by Douglas Adams) Some days ago I was talking with a friend about the infinite monkey ... [Read more...]

AND I HAVE A GREAT REJOICING DAY (mnemonic rule generated by mnemoneitoR for first 7 digits of Pi according to The Wonderful Wizard Of Oz) Is there some number impossible to memorize? Do not worry, here comes mnemoneitoR: the tool that you was always looking for! With mnemoneitoR you can translate ... [Read more...]

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 ... [Read more...]

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 ... [Read more...]

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 ... [Read more...]

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 ... [Read more...]

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 ... [Read more...]

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 ... [Read more...]

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 ... [Read more...]

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 ... [Read more...]

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 ... [Read more...]

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 ... [Read more...]

Music is the pleasure the human soul experiences from counting without being aware that it is counting (Gottfried Leibniz) I like the concept of sonification: translating data into sounds. There is a huge amount of contents in the Internet about this technique and there are several packages in R to ... [Read more...]

The heart has its reasons which reason knows not (Blaise Pascal) You only need two functions to draw a heart mathematically. The upper part is generated by (1-(|x|-1)2)1/2 and the lower one by acos(1-|x|)-PI. Here is how this heart is: Whats the area of this ... [Read more...]

Prediction is difficult, especially of the future (Mark Twain) Let me start with two important premises. First of all, I am not into football so I do not support any team. Second, this post is just an opinion based on mathematics but football, as all of you know, is not ... [Read more...]

I am strangely attracted to you (Cole Porter) Imagine a linear grid that extends to the left and right. The grid consists of cells that may be only one of these two states: On or Off. At each time step, the next state of a cell is computed as a ... [Read more...]

Computer Science is no more about computers than astronomy is about telescopes (E. W. Dijkstra) Some days ago I published a post about how to build fractals with R using Multiple Reduction Copt Machine (MRCM) algorithm. Is that case I used a feature of the grid package that allows you ... [Read more...]

Nothing in Nature is random … A thing appears random only through the incompleteness of our knowledge (Benedict Spinoza) This is one of my favorite mathematical mysteries. In 1991 David Boll was trying to confirm that the neck of the Mandelbrot Set is 0 in thickness. Neck is located at -0.75+0i (where ... [Read more...]

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 (Benoit Maldelbrot) Fractals are beautiful, hypnotics, mysterious. Cantor set has as many points as the real number line but has zero measure. After 100 steps, the ... [Read more...]