it should not be happy ending. i much rather have a happy beginning. cause there’s nothing like being absolutely relaxed to enjoy a good massage.

or better, what about “happy intermission”. build the tension, release, then the relax! that’s what it should be.

i read an article today with its title beginning with “Psychologists Find…”, which i read cause i found the announced findings really interesting, for their deep social impact. then half way the read, the article which seemed otherwise to be describing a legit study, revealed that the researchers have used a set of 110 people in their study.

now, i’m not a psychologist myself, but i am pretty sure that a population of only 110 samples, with no control group and certainly not sociocultural diversity is not considered a good enough group to extract conclusions AND publish them online for all us to read.

just cause i can find 110 people who own a car who can’t drink milk, it doesn’t mean i can publish an article “New Research Finds Owning A Car Increases Lactose Intolerance”. that’s not how science works.

who the hell is conducting these experiments and who’s allowing them to be published? and how did this end in my feeds?

Somebody in the very depths of the most apocalyptic part of the city’s decadent neighborhood, in a dark street hidden between shadows I find a house door protected unlike other doors. Rather than the usually security bars (yep, I know, doors with security bars…), this door has a design that my brain’s pattern recognition circuitry matches to some memory of mine from the past. It’s a familiar shape, a mathematical figure from my late teenage back from when coding fractals was my obsession. Once this parasympathetic alarm reaches my consciousness, I halt, turn around and look to the door. The doors motive is made after the bifurcation diagram of the Logistic Equation in the complex plane, which being a quadratic map, is holomorphic to the Mandelbrot Set (and it resembles it indeed). These are objects related to Fractal geometry and the Chaos Theory, trendy back in the 90s among computer aficionados. You might remember some of these words from Jurassic Park or from hippie american university teachers from those times.

I find it amusing that the designer of these door bars, and the owner of this house too, decided to honor this mathematical object. I also find amusing that I accidentally found it here, in the darkest corner of this (one must admit, very nerdy, city). 15 years later.

Inspired by the discovery, I run home and I code the fractal, which corresponds to the formula z -> h.z.(1-z), as if I was that 19 years old boy again. Only that this time I derive the formula for producing a smooth/continuous coloring in its exterior based on the Hubbard-Douaddy potential theory. Unlike when I was a late teenager, now I do have the maths knowledge to do so (although I am not as fluent as when I was at university).

The formula for the coloring is color = n – 1 + log2( log2|z| + log2|h| ), and this the realtime rendered set, together with the Logistic Map bifurcation diagram in real numbers superimposed (note how the bifurcation points alight with the periodic components of the fractal set):

as we all know, if there’s one kid/baby in the plane, (s)he becomes the dictator of the plane – by the power of crying (s)he decides when everybody else sleeps.

when there are two kids/babies in the plane… i have just learnt that they cancel each other (get tired of each other’s crying, indeed) and both fall asleep. and so can do the rest of us.

I just read this article where they try to explain what the privileges of being born in a wealthy (white) family are (I’m surprised this needs to be explained in the first place, but ok), and how it affects the american dream, which is, and I quote straight from the article, “everyone in the country has a chance to become wealthy and move into the upper class.”

I think this dream is pretty fucked up, and at the same time so internally accepted that these people don’t see the problem. To me, this ill-formed dream has already established that society will be divided in an lower and an upper class. As an axiom. I might be wrong, but as far as I understand the dream is not about having a wealthy and healthy country for all to enjoy, but to have equal opportunity to escapes the crappy lower class and saves themselves into the upper class. Basically, the dream is not to get rid of classes, but to be the one to be in the cool group (and “fuck the others”).

This article I just read aspires to open the eyes of those already in the privileged group by explaining to them how unfair it is that simply by being born in the right group the enjoy the luxury of encountering less obstacles to reach or stay in the social safety zone. And compassionate as the writer seems to think (s)he is regarding the lower class, the article totally misses the deeper unfairness, the real problem, the big elephant in the room.

I’ll copy&paste again, for your brain to shiver: The greatness of this country is that “everyone in the country has a chance to become wealthy and move into the upper class.”. Some are even proud of this. And that certainly makes this country unique. Not the way they think, though.

I sometimes feel these people got it wrong.

because repulsion can be attractive.

quick doodling on sphere again, but in this case on their dynamic, not their appearance.

making sphere repel each other in a stateless system where concepts such as force, acceleration and velocity don’t really apply (in their traditional sense of numerical integration).

click in the link to see the spheres repel each other in real time and to explore the code/maths involved in the animation/image:

in computer graphics coding, often times bugs manifests themselves as artifact of no little visual interest. it is really tempting to explode the bug and develop some semi-interesting visuals. and it can be an interesting exercise. in fact, i have a few times seen experienced art coders encourage young aspiring programmers use their bugs to create art.

however… i think this is not a good idea in general. and giving that advice can mislead the young apprentice.

sure the broken image it looks interesting. but the problem with bug-art is that most of the times the coder doesn’t understand the bug and hence the code/algorithm. and if one doesn’t understand it, one cannot control it. if you cannot control it, is it legitimate art? what’s the value of the art that you cannot direct? regardless this question, from a pure technical perspective, not being able to control your paintings/algorithms makes a poor graphics programmer.

once a bug happens and a visually interesting artifact emerges as a result of it, i think the best thing to do is to take a snapshot of the code/image, but keep moving and fix the bug. learn to control the image to be what (s)he wants. there will be time (and more creative resources) to make an image interesting (especially if it’s noise art) later in the game, no worries.

zoos. a concept from the 19th century.

i do understand that kids (and adults alike) from the London of 1850s had never seen an alive giraffe or an elephant in their lives, not even a moving picture (film) of them. i do understand that people would run to the zoo to see these fantastic creatures only seen in book drawing that were so different to the cows and sheep they were used too. and because of that, i do understand that zoos were visited every day.

but these days… we all have seen these animals in TV and in movies. so, can we stop going to the zoos. in fact, can we please stop having zoos altogether, and leave the animals where they belong?

if you are a city kid and feel like seeing animals alive, go to the country side and see a cow (have you ever seen, or milked a cow, city kid?). or if you really feel like seeing an animal from the savanna, go for a visit there and leave some money to fund the protection of their habitat.

stop going to the zoos. those things should most probably not exist.

Because we are all encouraged to do things the way we know they work, because reinventing the wheel is something we are supposed to avoid and because being stubborn is seeing as a bad quality… I often decide to hold to my believe that revisiting old stuff my lead to new ways to do things. Because I want so.

In doing so, sometimes, I do find, indeed, new ways to do things. Such as, rendering analytically antialiased spheres with analytical plausible soft shadows and occlusion.

Analytical in this case means not using montecarlo integrating any of these three forms of visibility. Or in other words, noise free, pixel perfect, light-speed images. Sure spheres are special, so what. They are cute too. So the time spent in paper and pencil with the formulas was totally worth it.

Realtime version and code/math, here:

i remember that back then, before the gps, couples often argued and fought when in the car. one of them was usually reading the (huge paper) map, trying to figure out where they were and which way to go. the other would be failing to follow the other’s navigation instructions. “you said ‘i think’ it’s left turn. that’s not an instruction!!”. “damn i told you clearly to turn left after the second tunnel, you don’t know how to freaking count?”

if you are above 30, you have seen this in your own family.

i think the gps have saved so many relationships.

if numbers like 0xA000, 0x3C8/0x3C9, 0xFFA6E, and 0x417 don’t mean anything to you, you are not old enough of a gfx programmer.

the fact that i can sit for 20 minutes and fix no less than two web vulnerability issues in our website, given that i am not a software engineer, nor i have a clue about the interwebs, and that i cannot but just copy&paste php, means that the internet technology is, in general, a huge pile of shit. period.

According to, I am a 35 to 44 years old woman who likes astronomy, maths and fashion, speaks English and Korean.

Well, I don’t speak Korean yet. Otherwise, spot on!

not related to any of the last two posts, i promise, this is the latest mathematcal image. improvised last night, it’s a 2D effect really, where a cylindrical projection is used to index a texture several times with different alpha cutoffs in order to create a stacked transparency thing. the usual color and fake lighting tweaking was the most difficult part as usual. since it’s a 2D effects, it’s really fast, so fast that i could implement some lens defocus.

Realtime animated version, with open code, here:

There’s a TED talk about the need for a new metaphor for sex.

Despite the good of the intentions in it, I cannot but wonder, over and over again, why the heck is there a need for a metaphor in the first place? There’s something intellectually unhealthy going on here. People, it is alright to talk about sex. Grow up already!

what are the side effects on men of the birth control pill?

has this experiment ever been conducted?

a heart attack is not an attack really. it’s more of a surrender.

Speaking of maths, the mathimage of this week is something mechanical and minimal. Totally improvised during a coding jam session after dinner. Mathematical image, animation and sound.

This is certainly slower than calling sin() and cos() directly in the GPU. But I find this code i wrote for a 6th degree Taylor approximation of sine and cosine pretty cute (from an aesthetical point of view).

vec2 mySinCos( float a )
    vec2 y = a + vec2(0.0,0.25);
    vec2 s = (fract(1.0*y) - 0.5)*PI;
    vec2 x = (fract(2.0*y) - 0.5)*PI;
    return -sign(s) * (1.0-(1.0-(1.0 - x*x/(6.0*5.0))*

I know there’s one too many 1s, and one too many PIs. But that’s part of the makeup.

Challenge for Laika: make a stop-motion animation of a character stop-motion-animating a character (fractal realities).

I know the cost is quadratic, and that the level-0 puppet need to be big… But if anyone can do it, that’s you!