Nifty Things

Heart

2012-02-20T18:15:00.002-05:00

A long time ago I made a heart symbol out of two sine waves in the standard 2 by 2*Pi ratio and two circles meeting at a 45 degree angle. The recent Valentine's Day reminded me of it when I saw other shaped hearts. I like this heart shape.

The Squareflake Fractal

2011-08-27T00:04:00.001-04:00

I sometimes doodle. Usually when in class or in a meeting. There's one doodle I've repeated a few times, drawing lines and refining rules until a nifty picture came out of it. It looks like this might be a fractal, or maybe a curve. I can't find any example of this fractal anywhere, so I'm calling it the Squareflake fractal. The Python script a wrote to draw these images is available here. The pictures are here.

{Edit}: My brother David was playing with my algorithm, and he found something - a Sierpinski triangle. If, when you make a vertical line, you only go down and no up, you get the triangle. You can also see it in the original fractal if you look for it.

The Ambiguity of Subtraction

2011-08-26T23:42:00.000-04:00

I was thinking about how subtraction is ambiguous (such as in A - B - C), and realized it only is if you consider the - symbol to usually be a binary operator, and not a unary operator indicating a negative number and addition of negatives. Here's my write up.

Better Music Visualization

2011-03-16T22:42:00.000-04:00

Made this a long time ago. Instructions are included. You have to convert your audio file to MIDI, and then my program creates a simple visualization based on the music.

Sudoku Solver

2011-03-16T22:38:00.000-04:00

Made this Sudoku solver a long time ago. Here is an example of loading Sudokus. The text file has to be in the same directory as the executable. I think I wrote it in C++. Should be able to solve easy, medium, hard, and some evil Sudoku puzzles.

Tone Generator

2011-03-16T22:31:00.000-04:00

This is a a little program that generates 1 to 12 different sine wave tones at the specified frequency, at the same time, for the specified period of time. Runs in Windows, from command prompt. Wrote it in C#. Good for trying out new chords not available on the keyboard.

Two Mirrors

2011-03-16T22:25:00.000-04:00

Here's a neat little script that shows a random line (made of a progression of a random-ish sequence of colors) being drawn, along with mirror lines across a vertical mirror, and horizontal mirror, and across both (the same as across a point mirror at the intersection of the vertical and horizontal mirrors). Oh, and the mirrors are also moving about randomly. This Perl script can't run in a browser, but you're welcome to try it on your own computer if you have Perl installed.

Capstone

2011-03-16T22:05:00.000-04:00

For my senior capstone to get my B.S. degree in Computer Science at the University of Maine, I wrote a fully assembly program to compress 24 bit bitmap images using SIMD, to see if speed improvements could be achieved from using SIMD. Here is my full capstone, with the paper and more. Or, you can view just the paper in your browser.

X Boxes

2011-03-16T21:54:00.002-04:00

Made this in 2D Design. I like how it came out.

Pi Digits and the Universe

2011-03-16T21:50:00.000-04:00

Question: Knowing the diameter of the observable universe, how many digits of Pi are needed to calculate the circumference of the observable universe, accurate to within 1 plank length?
Answer: 62 digits. Here it is: 3.14159265358979323846264338327950288419716939937510582097494459

The Effects of Daylight Saving Time

2011-03-16T21:37:00.000-04:00

When it comes time to set your clock ahead or back an hour, and you wonder why it's done and what it does, perhaps this graph can give you some insight.

Facebook Friends Graph

2011-03-16T21:23:00.001-04:00

If you graphed me, all of my Facebook friends, and all of their Facebook friends, what would you get?

I made a Python script to act like me and my web browser. I did look into using Facebook's API, but it doesn't allow you to see your friend's friend lists, and it doesn't even always get everyone on your own friend list, as people can block that feature of the API. When you use your web browser to log into your account and use Facebook, though, you do get all this information. So, I figured out the URL that the Javascript on the friends page used to display friends, 60 at a time. I had my Python script log into Facebook as me using urllib2, grab that data for me and all my friends, and parse the data using regex to get names and Facebook ID #s. Through a bunch of Python and Perl scripts, using YAML to transfer the data between scripts, I managed all the data in a dictionary of dictionaries, hashes of hashes, lists, and a custom Perl data type called Pairs that's like a hash with multiple entries for keys allowed. Oh, and I used Python's Pickle and CSV files too.

So anyway, me, plus my Facebook friends, plus all their Facebook friends equals 76,538 different people. I have 300 Facebook friends, and 44 of them do not allow me to see their Facebook friend lists. Graphing that made overly cluttered graphs with not much structure, mostly just flower looking groups. So I whittled the data down to only me, my Facebook friends, and their Facebook friends who are mentioned more than once (they are friends with at least two of my friends). This left just over 11,569 people.

The resulting graph is pretty. I would expect 5 groups: my family on my father's side, my family on my mother's side, my high school, my college, and a conference center I worked at for 2 summers. I'm not sure what the 3 groups that actually resulted are. I did make a 12 MiB SVG file with the names included in the graph, but I haven't found anything able to open the file without hanging yet.

To Give or Not To Give

2011-03-16T19:47:00.001-04:00

I don't know why, but I once asked, considering the percentages of the population who have each blood type, and considering which blood type can give to which, when someone asks themselves, "Should I donate blood?", how important is it that they decide "yes"?

To answer this question, you need to take three things into account: If you don't donate, how many people are there who could step in for you? How many people can take your blood? And, of those who can take your blood, how many other people can they take blood from? The following are the give scores from my calculations:

Importance factor that someone of this blood type decides to donate.

Higher score is more important.

O- ~~ 40.1

B- ~~ 24.7

A- ~~ 14.0

AB- ~ 10.6

O+ ~~~ 3.7

B+ ~~~ 2.1

A+ ~~~ 1.3

AB+ ~~ 1.0

Now, this calculation method is a little arbitrary, so if you're curious, here is the Perl script I used to calculate these scores. And again, these scores indicate the importance of an individual potential donator who is on the fence deciding to donate.

2 Point Perspective

2011-03-16T19:27:00.000-04:00

One day in drawing class I noticed that the method for creating one, two, and three point perspective drawings taught to me was not appropriate for all situations. Let's say you have a hexagonal nut that you want to draw lying on its bottom, with one of the corners facing you. Now, you could make a sketch of the nut's top in a square, then make a square in one point perspective, and warp the sketch from the normal square onto the perspective one. Or, for a stronger perspective, use a square with one of its corners facing you instead of one of its sides (some call this a diamond), and draw it in two point perspective (like the top face of this cube).

I have a better method. Just draw the hexagon with the parallel edges vanishing to three points on a line, or as I call it, 'line perspective'. My photo below of a perfect hexagon taken at an angle shows that this emulates reality. Two and three point perspective methods to make sense, as it's easy to place objects in two and three dimensional regular polygons that have edges parallel only to the dimensions that it's in (rectangles and rectangular prisms). But, if you are going to be drawing 2D and 3D regular polygons in perspective, it may be beneficial to understand line perspective and plane perspective (not sure if plane perspective can be used on a sheet of paper, though).

Split Screens

2011-03-16T19:07:00.000-04:00

Playing a two player game on an HD television can be quite annoying. Split screens are usually split top and bottom. On a 16:9 ratio screen, this leads to a 32:9 ratio for each player. That's over three and a half times as wide as it is tall.

So I tried creating alternative split screen profiles, with ellipses in each player's section indicating where most of the action should happen. In the captions, you'll see the width to height ratios and total areas of the ellipses.

Color Cube Slicer

2011-03-16T18:40:00.001-04:00

Around the same time that I was doing the Hilbert RGB Palette, I'm not sure if this was before or after I finished that, I was thinking about the problem of viewing the full resolution 3D RGB color palette, or Color Cube as I called it. Full resolution means 256 brightness levels for each of the 3 colors. This gives 256^3=16,777,216 different colored points.

And I was thinking, what if I took a sheet of paper, sliced the color cube at some chosen angle and position, let the cube paint the paper, took the paper out, and looked at it. What would it look like? So I made the Color Cube Slicer in Perl.

3 points define a plane, so I let the user choose 3 points in the color cube by specifying 3 different colors. The result is nifty looking images.

Hilbert RGB Palette

2011-03-16T18:24:00.000-04:00

So for a while, I was wondering: What is the perfect color palette? I was thinking about the color pallets provided with image editing tools such as MS Paint, GIMP, and Photoshop. I also restricted myself to the RGB color space, since that is the method of color display that computer monitors use.

Monitors have only three phosphors or crystals: red, green, and blue. When none are on, the screen emits no light (and it should also be poor at reflecting or scattering light). Red, green, and blue are chosen because that is close to the three types of color sensing cells you have in your eyes: red, green, and blue. When yellow light (photons with the energy to wiggle at a frequency of 517 THz) hits your retina, both the green sensitive and red sensitive cells are excited a little bit (or actually, I think they're calmed down). Your brain interprets this as yellow. When a screen wants to show yellow, it turns on its red and green crystals that are really really close to each other. Since these also excite your red and green sensitive cells in the same area on your retina, your brain thinks it's seeing yellow.

So anyway, RGB is a nice color space I think. Also, using 24 bit color is nice, since you get 8 bits, or 1 byte, per color. This lets you choose to have the crystal brightness be at any integer between power level 0 (fully off) and power level 255 (fully on). Nice and easy to work with.

Where was I? Oh yes, color palettes. There are a lot of different types of color palettes out there. I was wondering, shouldn't there be a naturally occurring color palette for the RGB color space? There is, but it's in 3D. Here's one construction I made of it, with only 3 brightness levels for each color. Start at the black square, and go up to turn on red. Then, go to the back right to turn on green too. this gets you yellow. Unfortunately, this color palette is 3D, so if I made one with 256 brightness levels for each color, you would not be able to see the colors inside the cube. The question became, Is there a 2D version or projection of this color palette?

Well, the property of the 3D palette that I think is the most important is that from any point in the palette, if you want a similar color, you merely need to move in some direction. It doesn't even need to be parallel to any edge. Colors are spaced from each other in a perfect reflection of the RGB color space. Can I preserve this locality feature in a 2D palette? Enter the Hilbert Curve. The Hilbert Curve is a space filling, locality preserving fractal curve. This means, if you take a string, and place it on a sheet of graph paper following the Hilbert Curve design to some order n, the string will touch every point on a 2^n x 2^n grid. That is the space filling property. Also, any two points that are close to each other on the string will still be relatively close to each other after the string has been placed on the graph paper. That is the locality preserving feature.

So, if I take a straight string, bend it into an 8th order 3D Hilbert Curve, dunk it in the color cube so that it is painted by the colors, then take the string out, make it straight again, and re-bend it as a 12th order 2D Hilbert Curve, I should get a 4096 x 4096 pixel image that is the desired color palette. It seems that Mr. Hilbert never described a 3D version of his curve. I found a few different versions a 3D Hilbert Curve, and chose to use the one that seemed to follow the spirit of the original 2D curve the closest.

Then it became a question of which direction to go: I could start the 3D curve at any of the 8 corners of the cube, each time orienting the curve 1 of 6 different ways (through rotation and reflection), and start the 2D curve at any of the square's 4 different corners, with each one having 2 different orientations. I decided to do all 6*8*4*2=384 versions. When I discovered how much hard drive space that would take, and how long it took my Perl programs to calculate and paint each image, I revised my decision and did only the 48 versions that could not be rotated or reflected into each other.

And the result is pretty. You can take any image and rotate or reflect it in any way, and it is just as correct. Try zooming in on the first one; it's quite nice. The 48 images take up 226.8 MiB.

The 6 different ones at the bottom are from when I wondered: What if I just paint the 12th order 2D Hilbert Curve with a simple incrementing RGB counter. Basically, start with black and slowly increase the brightness of the blue. Once it reaches full brightness, reset blue to fully dark, increase the brightness of green a little bit, and start increasing the brightness of blue again. continue for a long time. When green reaches full brightness, reset it to fully dark, and increase red a little bit. This can be done differently by starting with increaser green first, then blue, etc.

P.S. I just remembered that I already explained the Hilbert RGB Palette here. Oh well, if this one made no sense to you, try the other one.

Scrambler

2011-03-16T17:10:00.000-04:00

This one is really simple. After seeing the email going around regarding the order of letters in the middle of words being unimportant for the dozenth time, I wondered whether this was true, or if someone merely carefully constructed this particular statement. So I created Scrambler in Perl.

It takes the middle letters of each word in an inputted text (a news or Wikipedia article works well) as an ordered list of characters, randomizes the order of those lists, and returns the scrambled text. It is completely random, so 4 letter words have a 50% chance of being correct, 5 letter words 33% chance, etc.

My conclusion is that it depends heavily on the reading level of the original text, but otherwise it is mostly correct. But don't take my word for it; try it out yourself!

Gobbledygooker

2011-03-16T17:00:00.001-04:00

In a math class at the University of Maine - I believe Linear Algebra with Professor Hiebeler - the professor mentioned creating English sounding words or phrases using skewed probability tables based on sample text. A while later, I created the Gobbledygooker in Perl.

What it does is it takes a sample text (a news or Wikipedia article works well), removes non-(alphabetic or whitespace) characters, converts all letters to lower case and whitespace to spaces, and creates a probability distribution table answering this question: In the sample text, what is the probability that when you have character X followed by character Y, character Z is the next character, for all 27 characters (26 letters and 1 space). The number of rows in the table is up to 27^3=19,683. Calculating the probabilities is simple: If "ab" is followed by an "o" 4 times (say in the word "about"), by a space 1 time (the word "tab "), and never by anything else, then the probability that it's followed by an "o" is 4/5 = 80%, and by a space 1/5 = 20%. After making the table, the program then starts printing a two letter combo that is seen somewhere in the sample text, and then chooses the next character based on the previous two and the probability table. It does this for a while.

The result is a bunch of text that seems kind of like English, with correctly sized words, that is somewhat pronounceable, yet contains few real words. If you need a fake word for any reason, this is a good tool for inspiration. Go ahead, try it out!

My Blog

2011-03-16T16:32:00.000-04:00

This is my blog. I will not be posting news, my opinions, my personal life, stories, how-to's, reviews, announcements, or be taking submissions here. Rather, I will use this space to present nifty things I create and calculate. Updates will be infrequent and sporadic.