Today I attended a 3D Printing Workshop, where I had to design a 3D object with a for me totally unknown browser based software. After playing around with some shapes builded with polygonal pyramids I decided to start another design using a combination of rings.
I liked my creation so much, that I rebuilded it with a for me totally known text based software.
And this is the result:
The cells of a caterpillar morph to a shimmering butterfly.
This pattern are animated rings in a hexagonal grid with neon colors.
This pattern is based on a hyperbolic hexagonal grid.
This is the first official video of riding with the Trafo-Pop LED Jacket in Berlin at night on bikes.
This LED Jacket is illuminated by 100 LEDs.
Each RGB LED can be individually controlled to glow in one of 16 million colors.
The LEDs are connected to one Arduino Nano micro controller and powered by a rechargeable lithium battery, which can last a day and night.
Software (written by me) is running on the Arduino, which calculates colorful animations or shows predefined still images.
Take part at: trafopop.com
If you wanted to experiment with lamps in the past you had to choose those small 6 Volt light bulbs, which where used in the old wooden radios as backlight for the glass channel scales.
The same small bulbs are still used nowadays in bicycle tail lights. And there you can see at once one of the many problems of lightbulbs: They all shine in only one color, namely white.
But if you want to see red light for a bicycle tail light or for a traffic light, then you need for each color a separate color filter made of glass or plastic.
For coloring small glow bulbs you can manage this with a coating of dip lacquer, because they do not get too hot.
Maybe you can now imagine, what a sensation is was, for the first time to hold a precious Light Emitting Diode in your own hands.
The LED shone red, much purer than you were accustomed from the bulb. And all LEDs illuminated all in the same beautiful saturated red, more evenly than one was able with incandescent bulbs.
There were no LEDs in other colors. It took a while to that you also could buy green LEDs. But they where not as bright as the red LEDs.
And with the green ones yellow LEDs also arrived, because yellow can be mixed from red and green. Orange was also possible in this way, but it was not as popular. For home use red, yellow and green were at first enough to experiment with for example own traffic lights.
But what was missing for years, was a blue LED.
Meanwhile some automobile manufacturers started to replace the incandescent indicator lights in the dashboard with the more durable and thus more reliable LEDs. Only the high beam indicator light had do be a light bulb, because blue was required, until time finally for the first VW temporarily obtained a special permit and was allowed to equip vehicles with a yellow high beam indicator lamp.
Long since television remote controls with infrared LEDs had replaced the unreliable ultrasonic remote controls. But we hat had still to wait for blue LEDs.
In cities billboards were placed occasionally, with pixels of red and green LEDs that could shine in three colors: red, green and orange. Since the brightness of the green LEDs was improved meanwhile, but also the brightness of the red LEDs. This resulted in a mixed color of red and green, not yellow, but orange.
And then finally the right materials for the production of blue LEDs where discovered. In the beginning blue LEDs where really expensive. You could buy it. But they have hardly been used due to their higher price.
Thank to the blue LEDs it is now possible to produce RGB LEDs, where three LEDs (Red, Green and Blue) where combined in a transparent housing with separate wires to switch each color on and off separately. In this manner a RGB LED can also light up in Cyan or Magenta. Also white light is possible, if the maximal brightness of the color components is well adjusted.
Luckily the price of the blue LEDs dropped. And the manufacturers of electronic devices, such as monitor, PC or HiFi made it their fashion, now to incorporate distinctive blue LEDs instead of the previously often simple green power indicator LEDs.
The production of LEDs was now so well mastered that especially blue LEDs with a very high brightness were achieved.
This and the development of the white LEDs made it possible to use LEDs also for energy efficient flashlight and more and more for traffic lights.
This pattern reminds me of a surface of a leather sofa.
This are just some simple rotating lines in differrent colors, which can form a hexagon.
This is a reprensentation of the Newton Fractal 1-z³.
To make two-dimensional fractals, we need two-dimensional numbers.
Each xy-position on the screen is represented by a complex number which has two dimensions a so called "real" part for the x-axis and a so called "imaginary " part for the y-axis.
So each complex number c is the sum of this two parts and the imaginary part is distinguished from the real part by a imaginary unit called "i":
c = x + i * y
i is defined as:
i * i = -1
So we have an interaction between the two parts, which makes it graphically interesting, because both axes can influence each other by doing just a simple multiplication.
So why is this fractal called Newton Fractal?
Isaac Newton found an iterative method for calculation successively better approximations for the zeroes of a mathematical function.
The most simple function with three zeros is:
1 - z^3
Each zero of this polynomial function has the absolute value 1.
So the zero are all located on the unit circle.
One zero is at (1, 0), the other two zeroes are symmetrically located at 120° and -120°.
To get an image from the Newton Method, we need to color each pixel differently, depending to which of the three possible zeroes it converges.
Surprisingly the result is not a simple partition of the plane into three parts. The result is a fractal geometry.