• ## Taking advantage of the Symmetry of a Circle in Computer Graphics

Eh, late na pero sayang effort kaya sige na lang

If you were to create a program in that draws circle pixel by pixel, what would you do? Well, you can use this equation to get the points of a circle of radius $r$ and centered at $(h,k)$ as basis: $r^2 = (x-h)^2 + (y-k)^2$

Or, if we compute for $y$: $y = k \pm \sqrt{r^2 - (x-h)^2}$

Let’s try drawing a circle using C++11, OpenGL, and freeglut. We will use this as the template of our program. Note that we will be using GL_POINTS to represent pixels. (More …)

• ## Simulating Spiking Neural P Systems with Vectors, a Matrix, and the GPU.

WARNING: LONG POST

tl;dr Turing started it, Computational model based on neurons, Math magic, GPU magic

The Turing Machine is perhaps the most well known computational model out there. It is the theoretical basis of a modern computer which is one of if not the most important inventions of man. The Turing Machine however, is not perfect. There are some problem that are hard to solve using the Turing Machine, that is the problems that are in $NP$ but not in $P$assuming of course that $P \neq NP$.

Because of this problem, people started to look for ways around this problem. Alan Turing himself wrote papers, both published and unpublished, to move this effort forward. In one of his unpublished papers, he proposed two types of randomly connected neural networks with one key feature being the possibility of learning and training it to solve problems ; sound familiar? The same year he wrote about the former, he also wrote a paper proposing genetical or evolutionary search . But perhaps the most important  proposal Turing had in this effort is his idea of a machine beyond the Turing machine, this machine he dubbed the O-Machine which is basically a Turing Machine with an oracle that can solve any decision problem within a class of problems, such as $NP$, for free .

FUN FACT!

The paper where Turing proposed neural networks wasn’t published because his boss at the time dismissed it as a “schoolboy essay”. Do you know who his boss was? Sir Charles Darwin, not the Charles Darwin writer of The Origin of Species, but rather his grandson .

• ## hello_130.txt

Genesis Ian M. Palaganas. You can call me either Gen or Genesis.

What were your thoughts when you enrolled in this course?
♫ Hello darkness my old friend ♫ JK, non-discrete mathematics marami.

How comfortable are you with math?
Depends, what kind of math?

• Automata Theory, Discrete Mathematics, Similar topics
• 🙂
• A Spiking Neural P-System of degree $m$, is a construct defined as $\Pi = (O, \sigma_1,...,\sigma_m, syn, in, out), where$ […]. Wala lang test lang kung may latex dito
• Calculus and similar topics
• :): (mixed feelings)
• check natin ulit latex. The most beautiful equation in mathematics: $e^{\pi i} + 1 = 0$.

すごいいいい

What’s your dominant feeling right now?
Pain, as in physical pain. I’m still on medication for whatever that is that caused hyper acidity in my stomach and now I think a wisdom tooth is trying to come out and it hurts a lot. Currently living on Ibuprofen/Paracetamol. The first chance I get, I’ll go to UPM’s College of Dentistry; I heard dental services are significantly cheaper there.

c
Compose new post
j
Next post/Next comment
k
Previous post/Previous comment
r