Fibonacci:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...

Base-2 (2^x):
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, ...

Exponential (x^2):
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, ...

Comments Welcome!

Speaking of continuity [and mentioning sebi], i also want to say thanks to Daniel and Julia for being my photo models. And instead of writing a real introduction to this site, i’ll just post to the about category whenever i have an idea. And hello about tag.

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from boingboing:

Brickarms is an online boutique specializing in custom weaponry for LEGO minifigs. They offer both historical weapons as well as fantastic ones, like this M41A Pulse Rifle used the Colonial Space Marines. Even better, they’re all cheap—about a buck apiece.
Company Page [Brickarms.com]

I was thinking about getting some for my Lego Girl Brigade. But since i could only justify afford one ore two grenade-packs anyway, i decided to just continue teaching them diplomacy.

If we leave out the USB and power regulation circuitry from the official arduino schematics we have a quite simple setup that can still run your programs provided you power it from a suited source at 5V.

The reason for the 5V minimum is the external crystal @ 16Mhz. The datasheet for the atmega168 tells us at that the maximum frequency for the processor is dependant on your voltage source (page 305). So you need at least 4,5V to run it at 16Mhz in the “Safe Operating Area”. We don’t want to care why that is but conclude that if we want to run it at say 3,3 volts, we have to accept a slower performance and do some work.

Helpfully somebody did exactly what we want with an Atmega8 (before 168), and documented the steps at the arduino playground. The facts didn’t change for the 168:

• we can just ditch the crystal and its capacitors, and use an internal oscilator @ 8Mhz
• we need to burn a modified bootloader to the atmega, reflecting the new speed.
• “Safe Operation Area” now 2.7 – 5.5 volts

Burning the new bootloader:
The latest version of the Arduino IDE comes with a built-in “burn bootloader” function. It also comes with different bootloaders for the official arduino releases. The arduino LilyPad is actually exactly what we want to build, so hacking our own bootloader is not needed anymore. Just select “LilyPad” as a board type and “burn bootloader” from the tools menu. You’ll still need a supported programming adapter to the burning. Please see “Bootloader” on the arduino homepage for more details.

Note that you’re still able to use the Arduino IDE (Computer Software) to program the atmega as long as you have the LilyPad selected as a board type. At the moment all other boards are configured to run at 16Mhz, so the upload may work but your program will run twice as fast. (if you’re into making sounds, note also that 8->16Mhz is exactly one octave

The drawing shows the new schematic without an external oscilator. Just some powerlines and the obligatory pull-up resistor at the reset pin. The numbers name the arduino pin equivalent.

Though it seems relatively widespread to compare the invisible phenomenon of electrical current with the flow of water, most models stop where it gets complicated. To be honest, when i started tinkering with the first electronic circuits, i always imagined wires as pipes and current as water flowing through them. The problem was that i didn’t trust this image myself.

Current is just one parameter in a circuit, but then there you have voltage, resistance, capacitance, impedance, you name them. To make this short: It was the flat-mate of one of an old friend, who managaged to complete my picture in a five minute talk. That was about two or three years ago. And though i forgot her name, i still remember the great feeling of relief when she laid out her beautifully simple concept of electricity in front of us at the dinner table: Not only were wires pipes, but resistors were thinner pipes, and voltage the pressure in your reservoir. Of course a higher pressure would lead to a higher current. And absolutely understandable, too much pressure would break your pipe. [i have to note here that she, a student of biology, was really knowing what she was talking about, and her understanding of electricty wasn't limited to the analogy. ]It’s not the analogy itself that fascinates me here so much, but rather the fact that i didn’t dare to believe in such an “over-simplistic” concept before.

Of course any analogy is just that: an analogy and not the real thing. There are limits when comparing similarities of one system to another. Electromagnetism is just one example with no obvious pendant in the water world. In the end, knowing these limits is essential to understanding. They are features not bugs. Being able to pin point at system exclusive phenomenons may be even more important than the number of actual likenesses.