Would Like A Map Of The Whole Area, Just To Know For Sure I’ve Been To All The Places :)

Väldigt vackert när det är Mondrian målning som reflekteras om. Wow! Jag undrar hur en “grid” av rutor 1x1 skulle se ut efter den blivit omgjord.  Dags att uppgradera mina programeringsskills och göra egna program.. :)

Edit: Malin hade gjort ett fint program redan för detta. MEN, att rita raka stäck med mus är sådär halv lätt.. Resultat : 

When reflecting a painting in a circle, pen strokes close to the centre of the circle become thicker. Reflecting a pixel-based image would enlarge and distort some pixels.  A painting built of strokes, like a Mondrian-painting, is better suited for circle inversion.

 Paint Circle-Inverted Mondrian:

http://www.malinc.se/m/InvertedMondrian.php

Hey all. Here in Sweden some of our preschools teaches signlanguage. It’s a really good compliment and the kids rock it like they never did anything else. I know Swedsh signlanguage because of my sisters deaf kid. Its a wonderfful way to communicate. Love the bodylanguage that comes with it! Take care!  

Reblog if you think sign language should be taught as a language in schools.

Hey BAB, could you please share the code to this? Im on the way to learn some processing and this is the kind of code i would like to learn. So, please share, so i can learn from it :)

Take care mate!

rgb knot

Hej Malin. Hoppas du förstår svenska, annars kommer det på engelska under. Har du kvar koden till denna? Skulle så gärna vilja se en loop. dra ner hastigheten på den lite och se detaljerna lite mer. Tack på förhand!

Hey Malin. I hope you understand swedish, in otherwise i’ll write it in english below. Do you still got the code for this one? I would like to see it in a loop and slow down the speed a bit, just to see more details. Thanks in advance! Take care!

Tangent Circles

http://www.malinc.se/math/geometry/dothisen.php

Numberphile (https://www.youtube.com/channel/UCoxcjq-8xIDTYp3uz647V5A) Got some good videos on the subject.

Heres one that introduce the topic: https://www.youtube.com/watch?v=aqyyhhnGraw

Did you know that there’s a whole branch of topology called knot theory studying knots?

Find out more here: https://en.m.wikipedia.org/wiki/Knot_theory

Got to love Geometry!

The Complex Geometry of Islamic Design

In Islamic culture, geometry is everywhere. You can find it in mosques, madrasas, palaces and private homes. This tradition began in the 8th century CE during the early history of Islam, when craftsman took preexisting motifs from Roman and Persian cultures and developed them into new forms of visual expression. 

This period of history was a golden age of Islamic culture, during which many achievements of previous civilizations were preserved and further developed, resulting in fundamental advancements in scientific study and mathematics. Accompanying this was an increasingly sophisticated use of abstraction and complex geometry in Islamic art, from intricate floral motifs adorning carpets and textiles, to patterns of tile work that seemed to repeat infinitely, inspiring wonder and contemplation of eternal order.

 Despite the remarkable complexity of these designs, they can be created with just a compass to draw circles and a ruler to make lines within them, and from these simple tools emerges a kaleidoscope multiplicity of patterns. So how does that work? Well, everything starts with a circle. The first major decision is how will you divide it up? Most patterns split the circle into four, five or six equal sections. And each division gives rise to distinctive patterns. 

There’s an easy way to determine whether any pattern is based on fourfold, fivefold, or sixfold symmetry. Most contain stars surrounded by petal shapes. Counting the number of rays on a starburst, or the number of petals around it, tells us what category the pattern falls into. A star with six rays, or surrounded by six petals, belongs in the sixfold category. One with eight petals is part of the fourfold category, and so on. 

There’s another secret ingredient in these designs: an underlying grid. Invisible, but essential to every pattern, the grid helps determine the scale of the composition before work begins, keeps the pattern accurate, and facilitates the invention of incredible new patterns. Let’s look at an example of how these elements come together. 

We’ll start with a circle within a square, and divide it into eight equal parts. We can then draw a pair of criss-crossing lines and overlay them with another two. These lines are called construction lines, and by choosing a set of their segments, we’ll form the basis of our repeating pattern. 

Many different designs are possible from the same construction lines just by picking different segments. And the full pattern finally emerges when we create a grid with many repetitions of this one tile in a process called tessellation.

By choosing a different set of construction lines, we might have created this any of the above patterns. The possibilities are virtually endless.  

We can follow the same steps to create sixfold patterns by drawing construction lines over a circle divided into six parts, and then tessellating it, we can make something like the above.

Here’s another sixfold pattern that has appeared across the centuries and all over the Islamic world, including Marrakesh, Agra, Konya and the Alhambra. 

Fourfold patterns fit in a square grid, and sixfold patterns in a hexagonal grid. 

Fivefold patterns, however, are more challenging to tessellate because pentagons don’t neatly fill a surface, so instead of just creating a pattern in a pentagon, other shapes have to be added to make something that is repeatable, resulting in patterns that may seem confoundingly complex, but are still relatively simple to create. 

This more than 1,000-year-old tradition has wielded basic geometry to produce works that are intricate, decorative and pleasing to the eye. And these craftsman prove just how much is possible with some artistic intuition, creativity, dedication along with a great compass and ruler.

This slide is really something! :)

Video of my talk last week at ICERM, where I discussed a bit of my process for making GIFs. You can also access my slides here.

I’ll post more here: instagram.com/nathanwpyle

Take a deep breath. 

Time to take actions! We only got one place to call home, so lets act like its our home!

As governments discuss climate change in Paris, they’ll be referring to the dire predictions of climate scientists. Here are three visualizations of possible futures based on detailed climate models and summed up by the United Nations’ Intergovernmental Panel on Climate Change (IPCC) in their 2013 report. The deeper the red - the hotter things are getting.

The message is clear: we better act fast.

How did they come up with these models? Read or listen to Nell Greenfieldboyce’s story.

Image Credit: NASA’s Scientific Visualization Studio and NASA Center for Climate Simulation

Animal Gaits for Animators by Stephen Cunnane