Discovering 'tixy.land'

Software G'MIC
3

A bit more of this :slight_smile:

I thought of a “simple” way to add colors to those pixy.land animations, without having to write mathematical expressions that would generate 4D vectors, namely [r,R,G,B] , where r would be the radius of the disk, and [R,G,B] its color, defined at each point.
On the contrary, we want to be able to keep mathematical expressions simple, and be amazed to see that it generates complicated animations :slight_smile:

Also, the constraint I imposed on myself was to get the same animations as on tixy.land, with the same previous formulas.

So I simply considered that mathematical expressions should return complex numbers C rather than real numbers, with the following rules:

  • the module cabs(C) of the complex number C determines the radius of the disk at each point (x,y).
  • The argument carg(C) of the complex number C determines its color, in the form of a hue (the argument can be seen as an angle, so the HSV space is particularly adapted here).

I’ve also added a new variable z, shortcut for z = x + j*y, where j is the imaginary number [0,1] (i was already used in tixy.land expressions).

What is cool is that the original colored scheme is preserved : if the expression returns a real number (i.e. a complex C = [ r,0 ]), then cabs(C) = abs(r) is indeed the radius of the disk, and carg(C) = r>=0?0:pi so two different colors are still mapped regarding to the sign of r.
So, we get an equivalence with the previous (real-valued) formulas. This is nice.

Now, let me show you some simple examples below. As you see, the formulas remain simple, and we got full color rendering. Yipeee!! :slight_smile:

z_8_1

with the time variable t introduced:

ezgif.com-gif-maker (1)

And another one:

Nice, isn’t it ? :slight_smile:

4 Likes