Saturday, February 13, 2016

The Collatz Conjecture - Part 1

The Collatz Conjecture can be summarized as follows - Take any positive integer n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. The property has also been called oneness - Wikipedia

So, for starters, i decided to write a program that will compute the Collatz sequence for a 64 bit number i.e. from 0 to 18,446,744,073,709,551,615 which equals 264 − 1. After reaching the end of the cycle for a given number the program prints out the number N and the length of the cycle S. However, it does not print every cycle length, it only prints the next cycle that is greater than the previously computed cycle length.

The above code was compiled using gcc with full optimization. The executable was run on a 3.0 GHz Core i7 Quad with 8 GB RAM. The process priority was changed to SCHED_RR using the chrt command. It took the machine two weeks to generate the output shown below. The largest cycle sequence we were able to compute was 1428 for the 13 digit number shown. In the next part of this article i shall be posting details about running the same code on my NVidia GPU using CUDA along with some insane optimizations.

Oh, and there is also a short-film on the Collatz Conjecture...

Friday, February 12, 2016

Quadcopter Chronicles - I

So, i've decided to build my own drone from scratch. Here is a picture of the work in progress. The orange PLA chassis was printed on my 3D printer. It is going to be similar to the Crazyflie with a few modifications. So, why not buy the Crazyflie ? well, no fun in that...

So this is the X configuration. The slits have been cut into the motor housing to account for the error in the print caused by the 3D printer. I've observed with my printer that, if i give the hole diameter as 7.03 mm it always turns out to be less by around 0.2-0.1 mm, which is the error. When this happens the motors do not pass through the hole and i have to sit and file it which results in inconsistencies in the 4 holes.

By giving the same value of 7.03 mm is the diameter of the motor and a slit the motors can be accommodated in a tight fit by wedging the slit to allow the motors to pass though, removing the wedge causes the structure to wrap tightly around the motor due to it's elastic nature. 

Also there is something weird in the image below. If you figure it out leave a comment.

The body was designed in SolidWorks as shown below and weighs 9 grams. Yep, that is a lot of green, almost a relation fest, but i am learning to clean that up. Most of it is the symmetry relation due to mirroring the entities.

The motors and props are similar to the one used in the Crazyflie. The next task is to design the control system electronics.

If you would like to download the 3D STL model visit my Thingiverse link below:

Licensed under Creative Commons