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July 23 2014

February 02 2014

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Another interesting property of the logarithmic spiral is revealed if you roll it along a horizontal line. This animation shows the curves traced by points on the spiral, and note that the very centre follows the path of a straight line. The angle between this line and the horizontal is called the pitch of the spiral, and for our spiral galaxy the pitch is around 12 degrees. [more] [code

Reposted fromreckon reckon viasofias sofias

January 19 2014

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Reposted fromkatt katt viasofias sofias

January 18 2014

Reposted fromqb qb viasofias sofias

December 21 2013

December 15 2013

Is this a new way of bringing the Mandelbrot set to life? Each number on the complex plane, c, is repeatedly squared to give a new value, and then added to the original value c. This gives a path for each c that takes it around the plane. Those that don’t run off to infinity are in the Mandelbrot set. This animation allows the c to move along its path, and colours the plane at the starting position c with the colour of the plane at the end of the path. The plane is coloured so it is black everywhere with a rainbow disk in the centre [so at time 0, when the points haven’t started moving, we just see the rainbow disk]. As time progresses, after a series of bifurcations and pulsing beats, we see the familiar Mandelbrot set take form. [interactive] [code] [more]
Reposted bysofiasincontrovertibleRK

October 16 2013

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One side of a triangle slides over the coordinate axes, so the third vertex describes an ellipse. Depending of the characteristics of the triangle, ellipses of different sizes and orientation are described, including the cases of degenerates triangles of zero height, which generate ellipses with vertices over the coordinate axes; and the case of an ellipse degenerated into a segment, when the triangle is a right isosceles one.

Los lados de un triángulo se deslizan sobre los ejes coordenados, de manera que su tercer vértice describe una elipse. Dependiendo de las características del triángulo se generan elipses de distintas dimensiones y orientación, incluyendo los casos degenerados de un triángulo con altura 0, que genera una elipse con vértices sobre los ejes coordenados; y el caso de la elipse que se degenera en un segmento cuando el triángulo es isósceles rectángulo.

Idea basada en el applet “Generación de una elipse" de la exhibición Imaginary (y recomendada por ^DiAmOnD^, de Gaussianos.com).

Este post participa en la Edición 3.14159 del carnaval de matemáticas en español, cuyo anfitrión es el blog Scientia

Reposted frombwana bwana

September 09 2013

Reposted fromqb qb viaresa resa

June 09 2013

How do Centrifugal and Coriolis forces affect the motion of particles as the speed of rotation is varied?  This animation shows how the underlying grid of my previous post is warped at differing speeds of rotation. Note the square grid when there is no rotation. [code] [video]  
Reposted bysofiassofast
The creation of a fractal Brownian tree.  Particles move around on random walks, but can become stuck starting at a seed in the centre.  This creates intricate patterns similar to those created in certain chemical reactions and electric discharges. [more] [code]
Reposted bysofiasGretelsofiasNorkNorkdarksideofthemoonrainbowzombieskilledmyunicorn02mydafsoup-01hashn0g919youamburningensoTokei-Ihtovolldostspinatlasagneroritasl420apertureYggryeglerion-justforfundafilMrCoffeLogHiManowisgoodjosephineregcorddonotsendrequeststonerrTomred97WeksadremdicoMeraristraycatschrodingersdogyouamfretkatfDerOrwischerpapajofafnirscavekrybuskaparQudaciturionBertIsTheWordczarna-owcaArtifexExMachinaTomred97xalzEveR
Disks moving in a square grid trace out an interesting pattern as they pass over a rotating wheel.  Some traces appear to go towards the centre only to be flung back out, in some cases forming a sharp corner. A few of the traces form loops, as if there was also a force acting sideways rather than outwards.  This demonstrates how the Centrifugal and Coriolis ‘forces appear to affect the motion of objects in a rotating frame. [making of video (new)] [more] [code
Reposted bysofiasfpletzbrightbytewekstestGretelarenlordminxcygenb0ck02mydafsoup-01arabuslvcksburningensojv6gruetzeylem235sixtusfrittatensuppefiffeycoloredgrayscalenaichapfelstrudlmasuochaDiviusbeneimamotherfuckingsharkbitch1317nanokneeamaxoxo4stefan2904mihaicontinuum02mydafsoup-01volldostzycienakrawedzipilkunnussijaorchilacorrode
natural logarithm expressed as integral of 1/x
Reposted bysofiasjemkartofletoniewszystkoRekrut-K02mydafsoup-01kosmikloveMrWasp

March 10 2013

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Reposted from1NdyGo 1NdyGo viaclifford clifford

February 07 2013

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a play on kites and symmetries
Reposted fromeigenvalue eigenvalue viamondkroete mondkroete

January 21 2013

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Icosahedrons are actually the basis for Spherical Quad Trees (SQT) used in computer science for spherical data. Every triangle can be easily split into four triangles of equal area. You have no special points like the poles or a split between 360° and 0° and so on. Each "Trixel" can be handled the same way as anyone else. You can also easily adapt these recursive splitting depending on the details you need.
Reposted fromshallow shallow viasofias sofias

November 20 2012

A Cardiod, a lovely mathsy heart shape, can be constructed as shown in the animation as the combination of many circles generated from a single underlying circle. This shape describes the sensitivity regions of many directional microphones.
Reposted fromscience science viamondkroete mondkroete

October 19 2012


A wave and a circle are both two-dimensional projections of a helix.

Reposted fromnerdanel nerdanel viamondkroete mondkroete

October 15 2012

Play fullscreen
a logical element in rod logic, forming an and-, or-, and xor-gate.

as part a project to build a Babbage-Boole Rodulator or Logical Engine, a binary mechanical universal computer.
Reposted fromsofias sofias

September 10 2012

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Reposted frommjidamini mjidamini viamondkroete mondkroete

September 01 2012

construction of a pinwheel tiling
Reposted bysofiasbrightbyteadamski02mydafsoup-01appleinthebrewsofastkhabarakhqvarfafnirscavemondkroeteMadMaidfusobollabollaToshioTV
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