five times a

analyzing architecture at any angle

Month: October, 2015

/code/txt/ Apollonian Gaskets in Python

Apollonian Gaskets are fractals that can be generated from three mutually tangent circles. From these, more circles which fill the enclosing circle can be calculated recursively.

I implemented this in python as a command line program that saves those as svg images. Below I will explain the math behind it and show some images.

1   How it works

The process of generating an Apollonian gasket roughly works like this:

We start with a triple of circles, each of which touches the other two from the outside. Now we try to find a fourth circle that is also tangent to each of the three. It’s easy to see that there are two possibilities for this: Either it lies in the middle of the three given circles (externally tangent) or it encloses them (internally tangent).

Figure 2: Three and four mutually tangent circles

Left: Three circles with different radii. Each is tangent to the other two.

Right: Two possibilities for a fourth circle that is tangent to the first three. Externally tangent (pink) or internally tangent (green). Read the rest of this entry »


/txt/ ‘In the future we will wear robots,’ says MIT ‘bionic’ professor

Hugh Herr, who heads the Biomechatronics research group at the MIT Media Lab and has been dubbed ‘the leader of the Bionic Age’, took to the stage at DigitasLBi’s New Front conference to discuss the potential of a “transcendent human”.

Herr told the story of his transformation from double amputee after a climbing accident, to exceeding what he was previously physically capable of on the rock face.

With technology I am released from these shackles of disability – we will end disability in this century

Herr was told by doctors that there were many things he would never be able to do in life, let alone ever climb again. However, 24 hours after hearing that news he decided the doctor was wrong.

“Technology is not invariant; it’s being upgraded all the time. My body was completely fine, beautiful and powerful. The only hold back was technology and bad design. Technology changes and we can innovate. I climbed at a superior level after my limbs were amputated.”

In the future we will ‘wear’ robots

We will design nature and change nature under our own power – we will give ourselves new bodies

Herr said he embraced the challenge of what his new limbs could be, thinking of a “bionic limb”, rather than a fake-looking human false leg.

“I can be any height I want – think Inspector Gadget. I could climb where no one had before, with three-metre legs. A few people actually said ‘you’re cheating’.”

Herr said it was within our capabilities to fundamentally transform the biological brain and body, extending the sensory experience. He painted a picture of using technology to enhance our bodies.

“We will design nature and change nature under our own power. In the future people will be wearing robots. You don’t need a missing leg to exploit this technology – we will give ourselves new bodies.”

New identities: we are plastic and malleable

Herr said that in 30 year from now, everyone will be able to modify and sculpt their bodies in a way they see fit.

If you look at a photo after my legs were amputated, do you see the potential for a human who will go beyond human capability?

“Our bodies are plastic and malleable, our very identities are plastic and malleable. A year after I was told I was crippled, I was even more powerful and strong.

“If you look at a photo of me after my legs were amputated, do you see the potential for a human who will go beyond human capability?”

Herr believes that “disability will be overcome” through creativity and innovation.

“You can’t, with a straight face, say that I’m disabled. With technology I am released from these shackles of disability. We will end disability in this century.”

Herr concluded: “In the future, humans will experience a transformation in how they sense, think, feel and move. I dream of a world without disability; I ask you to dream with me.”




/vid/ How to Grow a Mind: Statistics, Structure and Abstraction




/vid/ ARM CMO Ian Drew Keynote (Computex 2015)




/vid/ Future of the Network Documentary, Part 1 – M2M and the Internet of Things: Brace for Impact