Infinitized (Sierpinski) fold using bitwise operators

[DarkBeam]

This type of fold is totally new.
The idea is to add a fractal level to Tglad's Mandelbox without heavy job for the CPU.
To do so we could exploit the floating point structure that is "sierpinski like" if you think about it. (Yes really I am that insane )

In fact fp numbers are structured like...
(Sign)(Exponent)(Mantissa)

If you can fold the mantissa preserving the exponent you can get a fractal fold  

It is definitely not as easy as it seems too bad.

But I was able to do it! Now suppose to define some constants. If you use doubles, they must have the same size. But you set directly their bits not their value!
SEXP contains the bits of Sign and Exp. all on. If you use double they are dwords in 32 bit machines. So SEXP = 0xFFF00000 00000000
SEXP_parity is its "parity bit"= 0x00100000 00000000
Nbits is the number of bits turned on in SEXP... but - 1. Count them

Okay so... the code is this

Code:

x = x / foldl; // user defined
const SE1 = 1.0f and SEXP;
const mantissa = not SEXP;
// x is a coordinate you want to fold
if (x>2 or x<-2) {
   m = SE1 xor (x and signbit); // you can really find signbit DON'T YOU :D
   n = x; // Save the sign without splitting
} else {
   m = x and SEXP;
   n = x and mantissa;
   n = n xor SE1; // Split x in two parts
}
n = abs(n);
n = 0.5 - abs(x-1.5);
// but we must restore sign and exponent so...
x = m * n;
m = m and SEXP_parity; // or SEXP for that matters?
shl( m, Nbits ); // make it a sign shifting bits
x = x xor m; // now it has alternate signs DONE!
x = x * foldl;

Very hackish. And proud enjoy!

[cKleinhuis]

so, where is the pretty picture

[DarkBeam]

 

Too bad I haven't got it because MB is not a function plotter

I cannot even post a picture of the fractal because I am using my tablet now

Btw it's the fold used in Amazing Surf 2 (latest version)

[KRAFTWERK]

so, where is the pretty picture

I like the code! 

[DarkBeam]

Here is a picture (hopefully pretty? Chris?  ) - btw, here fold is different from the one illustrated above!

The fold center is moved to the borders before applying infinitization. The result is awe (I think)

[quaz0r]

mmm its pretty 

[knighty]

Looks good!

[DarkBeam]

Thanks again fold genius