Torn Asunder

[Fractal Ken]

Strange attractor
x_n+1 = tri(1.77x_n + 3.11) + tri(-2.67y_n + 1.63)
y_n+1 = tri(1.31x_n + 0.85) + tri(0.84y_n - 1.40)

tri is a periodic triangle function. I formed it (conceptually) by connecting the extrema of the sine function with line segments.

[Alef]

What is triangle function? Haven't heard that thing.

But nice triangular crystals in pseudo 3D. This aren't artistic, just pink background, but looks having artistic potential.

[Fractal Ken]

What is triangle function? Haven't heard that thing.

I just meant this pattern repeated from -Infinity to +Infinity on the horizontal axis:

[Dinkydau]

Oh, it's just that. I was confused too.

[matsoljare]

I've used the triangle function for various 2d images before, here's how i define it:

abs((x-int(x))-0.5)

[Fractal Ken]

I've used the triangle function for various 2d images before, here's how i define it:

abs((x-int(x))-0.5)

Neat! That's very succinct and gives the right shape for positive x. At least on gfortran, the int function behaves in a funny way for negative x; for example, int(-1.9) = -1. So I'd need to use abs(abs(x-int(x))-0.5).

[Alef]

But then triangle function is not a abs(abs(x-int(x))-0.5), becouse resulting maximal value of this thing is 0.5, quite bad for colour transfer function.  :

More something like this, then throught it will have different period and all positive (good for colour function):
abs(abs(x*0.5-int(x*0.5))-0.5)*2

[Fractal Ken]

But then triangle function is not a abs(abs(x-int(x))-0.5), becouse resulting maximal value of this thing is 0.5, quite bad for colour transfer function.  :

True. Notice I wrote "gives the right shape for positive x" rather than "gives the right result for positive x" in answering matsoIjare's suggestion. The following adaptation reproduces the graph from my earlier post:

v = x/(2*PI) - 1/4
tri = 4*abs(abs(v - int(v)) - 1/2) - 1

[Aexion]

Hello,

Try this:
f(x)=asin(sin(x))*(2/pi)

http://aexion.deviantart.com/art/Sin-268786434

 

[cKleinhuis]

Hello,

Try this:
f(x)=asin(sin(x))*(2/pi)

http://aexion.deviantart.com/art/Sin-268786434

 

ehrm,  @aexion, you dont have an animation of a flame or a mandelbulb showing the fun you propose
you know i am LOVING such fun!

[Fractal Ken]

Try this:
f(x)=asin(sin(x))*(2/pi)

Nice idea, but calls to sin and arcsin for evaluating a piecewise linear function? Don't let your computer science professors see this.

[Aexion]

ehrm,  @aexion, you dont have an animation of a flame or a mandelbulb showing the fun you propose
you know i am LOVING such fun!

Thanks!, I think that I have some renders here, just let me find them.. 

Nice idea, but calls to sin and arcsin for evaluating a piecewise linear function? Don't let your computer science professors see this.

Perhaps.. but there's some hidden art on it.. lets see:
f(x)=asin(sin(x))*(2/pi)
if you want a cosine-like triangular, it is:
f(x)=asin(cos(x))*(2/pi)

But what happens if you change it a bit (like adding another sine), so you get:

f(x)=asin(sin(x+sin(x*4)))*(2/pi)

You get an interesting cyclical function, like the sine and the triangular function, but with several bumps more..
the "cosine version" is:
f(x)=asin(cos(x+sin(x*4)))*(2/pi)

Now use it on your favorite fractal that has sines and cosines (replacing them with these versions) and you will get some interesting fun.. 

[Fractal Ken]

But what happens if you change it a bit (like adding another sine), so you get:

f(x)=asin(sin(x+sin(x*4)))*(2/pi)

You get an interesting cyclical function, like the sine and the triangular function, but with several bumps more..
the "cosine version" is:
f(x)=asin(cos(x+sin(x*4)))*(2/pi)

Now use it on your favorite fractal that has sines and cosines (replacing them with these versions) and you will get some interesting fun.. 

Cool! I'll have to play with those formulas.

[Alef]

I was searching wikipedia for functions, they had something like 'least used mathematical functions' or something like that.
There were some sine waves on sine waves like this thing with two sines. So far from lest known functions I found usefull haversine and sigmoid functions, but triangle function alsou worked quite nice as colour transfer function. 2 sines and arcine could be a bit too slow.
There should be lots of:
http://en.wikipedia.org/wiki/Category:Special_functions
http://en.wikipedia.org/wiki/List_of_mathematical_functions
And a wikipedia alsou uses sine arcsine.
http://en.wikipedia.org/wiki/Triangle_wave