Gielis Shapes
Project: The Total Library

In 1997 the superformula was discovered, which solved the problem of the limited symmetry of superellipses and supercircles. Supershapes like pentagons and starfish, triangles and rose sepals, flowers and leaves, can now be described by a single equation, based on the generalization of Lamé's supercircles and superellipses.

The key step from Lamé’s supercircles was to convert the equations to polar coordinates and to add a single parameter for symmetry. It was extended into three dimensions as well.

This discovery was published in the book “Inventing the Circle” (2001, 2003) and as Invited Special Paper in the American Journal of Botany in April 2003. Worldwide awareness was created by websites such as Nature Science update, Science News Online, and Wolfram’s Mathematica website.

Supershapes were introduced later in the field of geometry under the general name of Gielis' curves, surfaces & -transformations, also in higher dimensions.

Quoted from GIELIS' CURVES & SURFACES


Bram Stolk, author of the Superformula Shape Miner for iOS writes:

Superformula was created to have fun with mathematics. Anybody can explore the colorful universe of shapes described by a powerful formula.

The Superformula, or Gielis-formula was first proposed by Johan Gielis. The formula can be used to define a wide range of shapes, including shapes that occur in nature.

When describing shapes in three dimensions, two instances of the formula are applied, each with 6 parameters. This results in a 12 dimensional parameter space in which a multiverse of interesting shapes reside.

The Superformula app is developed as a tool to mine this 12 dimensional parameter space. By swiping your finger, the space is explored, two parameters at a time. The strength of this application comes from the lightning fast calculations used to determine the shapes. The app uses an OpenGL-ES2 vertex shader to compute the shapes on the graphics hardware of the device. This means zero wait, and instant visualization of the Gielis-shape.

User Interface of the Superformula app


More

EXPLORATIONS OF GIELIS CURVES & SURFACES by Genicap

Using the Super Formula for building Super-Antennas by Blue Economy

Sun, Jul 22, 2012  Permanent link
Categories: science, technology, thrivability, visionary, sustainability, research, economy
Sent to project: The Total Library

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If we are only teaching what we know...
Project: Polytopia, The Total Library

... our children can only do as bad as we are doing, and this is the challenge we are facing - we have to go beyond it. — Gunter Pauli

Click image for video

Quoting more for context

Forget about the fact that while we were doing in the past the right way is going to bring us to the future.
It is not
and this is one of the biggest lessons we have
as parents, we want our kids to be better
and here is a picture of my little baby
and my two sons
we always want it to be better but that means that we have to create the space of our children
can invent, develop new pathways to the future
Because if we are only teaching what we know
our children can only do as bad as we are doing
and this is the challenge we are facing
we have to go beyond it.

...

My quest today is to see how can we design a new competitive model
a business model based on sustainability whereby we define sustainability
as the capacity to respond to the needs of all with what we have
and that's the way natural systems do it all the time
the past twenty years we've been doing things…
that we thought were the normal way to do it
but it was an economy that was based on what we did not have
and so what do we have?
well, first of all we have a lot of needs
and since there are so many unmet needs for water, for food, for healthcare, for housing
there is a growing demand, even at a time of a recession
and we have the science to develop it
so much of the science is available
and we don't use it, it gets buried
so how do we achieve a sustainable society?
we achieve a sustainable society when first of all, we think positive
that's what this conference is all about
think positive
second, learn creatively
and third, if any one of you thinks this meeting is a success
it is because when you go out of this meeting you do something
too many meetings are talk shops
too much talking, no action
dream it, don't do it
that's unfortunately what we hear too often
so my work today, is very much focusing on doing all of this at once

...

More from Gunter Pauli's TEDxTokyo talk, with full transcript on http://dotsub.com

Sun, Jan 1, 2012  Permanent link
Categories: introduction, science, thrivability, future Polytopia, visionary, learning, education, sustainability
Sent to project: Polytopia, The Total Library

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