Title: Escape time versions of IFS Post by: msltoe on April 17, 2011, 09:16:03 PM I've been looking at escape time versions of simple IFS fractals. This should help us think about the more complicated ones and 3-D versions. No claim of originality.
Here's the code and then a few pictures: x=real(z);y=imag(z); x=abs(x);y=abs(y); x1=x;y1=y; //Shape to be carved out of square // if ((x1<0.5)&&(y1<0.5)) {x=100;} // Menger if ((y1>0.5)&&(x1>0.5)) {x=100;} // Viscek Cross // if ((x1>0.875)&&(y1>0.875)){x=100;} // Thicker cross //Bounding square if (x>1.5) {x=100;} if (y>1.5) {y=100;} //Shifting x1=floor(x+0.5); if (x1>1) {x1=1;} y1=floor(y+0.5); if (y1>1) {y1=1;} x=x-x1; y=y-y1; //Rotation x1=a11*x+a12*y; y1=a21*x+a22*y; //Scaling x=3*x1;y=3*y1; // For now, pixel = 0 z=x+flip(y); z=z+pixel; Title: Re: Escape time versions of IFS Post by: visual.bermarte on April 18, 2011, 09:54:01 AM Hi, sorry but
what is it a12 and a22? 2 parameters/sliders maybe? and pixel? flip,real and imag are already defined somewhere else? :embarrass: thanks in advance Title: Re: Escape time versions of IFS Post by: msltoe on April 18, 2011, 02:54:48 PM visual: A = [ a11 a12 a21 a22] A is a matrix transformation. In order to be conformal, it has to be a rotation matrix times a scalar. In the 1st and 2nd pictures, A is the identity matrix. In the 3rd, it is a rotation of 45 degrees. The pixel is zero in all three pictures. It's hard to find interesting patterns with pixel > 0. -mile |