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Well, it definitely has been a while. A quite long while it has honestly. In this blog post I'll explain you what's going on with me and how things in regard to Gamemode 4 and the wiki will change. Plus, I'll have a 'quick' reaction on the famous Math stuff Penguin puts on his profile page: you should definitely check it out if you haven't already.

Where have I been?

You guys might remember me as one of the more active persons on the wiki! And I wish I still could be. However... School just happened xD

I've been most active during my whopping 3 month holiday after my final year in secondary school and sadly, all holidays come to an end at some point. But that doesn't necessarily mean I can't be online anymore, or could it....? Well, I've started university 5 weeks ago and my god it's demanding a lot of time! As a mathematics and computer science student I just simply don't have any time to play some games; at most to check Reddit, a select amount of YouTube videos and scroll maybe a bit though the wiki activity. But that's it! And don't think I'm not enjoying. Oh hell no! I'm loving it. Though sometimes all the work overwhelms me. It's tiring - but probably the best time of my life!

This basically means I can't be online that often on the Gamemode 4 wiki. :'(

So, what will change?

Will I be leaving this place? HELL NO! I love you all too much to leave, though I will have way less time to spend here. I'll try to keep the discussion alive on here and to read as many of the forum posts I can - but not as much as you probably are used of me. So don't worry! I won't be leaving, I just need some more time for myself from now on.

And now... the fun stuff!

Re: Maths Stuff

I just saw Penguin's Math rubric in his blog and my mind went crazy! I love Maths. Just love it! Just to clear away some prejudices: No, math's not just about numbers. Yes, mathematicians have humour. Yes, mathematicians (and especially computer scientists) are amazingly social people. Yes, maths is fun!

Now that's out of the way: Let's start rolling!

#001 Sierpinski's triangle

Like penguin already told you: those are magical shapes that I mostly refer to as a triforce in a triforce in a triforce in a triforce. In maths - all figures that are created using a similar manner are called fractals. Plus, there's something really weird going on with fractals regarding their surface and perimeter. Let's take a look at the triangle's surface first.

Surface and Perimeter

Like penguin told in his post: each generation of the triangle, it's surface gets multiplied by ¾. If we keep doing that for all the new triangles for n amount of times approaching infinity (basically repeating cutting out chunks for ever), we get the following surface:

\lim_{n \to \infty} {\left(\frac{3}{4}\right)}^n=0

Yes; the surface of the triangle is theoretically 0. But if we take a look at the perimeter: you notice that the perimeter grows with one third every time. So for the perimeter (if you repeat it an infinite amount of times) you'll get:

\lim_{n \to \infty} {\left(\frac{4}{3}\right)}^n=\infty

This means that the Sierpinski triangle has an infinitely large perimeter whilst having no surface. Weird isn't it?

The Chaos Game

Another weird thing about the Sierpinski triangle is that is is everywhere. One of the ways to create the triangle is by playing the chaos game. In the chaos game you draw a triangle and call each corner either (1,2), (3,4) or (5,6). Now just draw a dot randomly inside the triangle and repeat the following:

  1. Roll a dice.
  2. Draw a dot exactly between the corresponding corner of the triangle and the previously drawn dot.

Once you've done this for enough times: you'll get... guess what... the Sierpinski triangle! This way you can plot the triangle with only a few lines of code! The triangle below is the one I plotted myself using this method:

Triangle







Pascal's Triangle
PascalTriangleAnimated2

Pascal's Triangle

Pascal's triangle is a triangle where the top number is 1, and each number below it is the sum of the two numbers above the number. Sounds confusing? Take a look at the picture to the right. The weird thing though: is that if you colour in all the odd numbers you'll again get the Sierpinski triangle. Just try it out for yourself (I swear! DO IT NOW!) and be amazed.

Random Homework Assignment

A few weeks back I had to do a homework assignment for Programming. I had to make an automaton... When I tested the harder part of the exercise I just put in some weird number and guess what I saw as output:

SierpinskiOutput












Yes. The FLIPPIN' TRIANGLE again. Maths's lovely isn't it ;)?

#002 Sorting Algorithms (bogo sort and video)

I'd like to indroduce you to my favourite sorting alogirthm of all time: BOGOSORT. Why is it so special and awesome? Because it's practically useless! So now I hear you wondering: what is bogo sort? Well.. Let's take a closer look then!

Bogosort

Bogosort works like this: suppose you have a deck of cards and want to sort it. Repeat the following until you have a solution:

  1. Throw all the cards to a wall.
  2. Pick them all up.
  3. Check if they are in order.

Yes. This is slow and should never be implemented. To give you an idea of how slow it is, I made a little program that sorts n integers in a list using bogosort. Unofficial benchmark is on a intel i7:

Took 1ms for 1 elements.
Took 0ms for 2 elements.
Took 1ms for 3 elements.
Took 0ms for 4 elements
Took 0ms for 5 elements.
Took 2ms for 6 elements.
Took 2ms for 7 elements.
Took 74ms for 8 elements.
Took 35ms for 9 elements.
Took 178ms for 10 elements.
Took 13493ms for 11 elements.
Took 830703ms for 12 elements.

You can make your own conclusions!

Fun video to visualise sorting algorithms

Give it a watch! Much beeps and colours: great visualisation of how all the sorting algorithms sort.

15 Sorting Algorithms in 6 Minutes05:50

15 Sorting Algorithms in 6 Minutes













Love

That's it for now! Cya the upcoming days and maybe during the community UHC!

<3 Caney

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