Publications by @aschinchon
The Music of the Spheres
Tweet He himself could hear the harmony of the Universe, and understood the music of the spheres, and the stars which move in concert with them, and which we cannot hear because of the limitations of our weak nature (Porphyry, Life of Pythagoras) I love legends. The life of Pythagoras is riddled with them: from the discoverie of consonant inter...
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Building Affine Transformation Fractals With R
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 Koch curve created from a 1 inch segmen...
1969 sym R (589 sym/1 pcs) 12 img
What The Hell Is Pi Doing Here?
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 two biggest circles meet each other). He tr...
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I Need A New Computer To Draw Fractals!
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 to locate objects easily into the viewPort avoiding to work wi...
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Cellular Automata: The Beauty Of Simplicity
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 function of its left and right neighbors and the current state of the cell itself. Given one cell, if t...
1810 sym R (628 sym/1 pcs) 18 img
Why I Think Atletico De Madrid Will Win 2013/14 Spanish Liga Of Football
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 an exact science. Football is football. This is a good moment to analyse Span...
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Shoot The Heart With Monte Carlo
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 heart? It’s easy: integrating heart.up(x)-heart.dw(x) between -2 and 2 and you will ob...
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The Sound Of Mandelbrot Set
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 help you to sonificate your data. Maybe one of t...
3634 sym R (2592 sym/1 pcs) 14 img
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 dimensions. Since images a...
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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 I worked also with images showin...
2043 sym R (1760 sym/1 pcs) 18 img