This pic is the biggest I have done by a long way. I actually did it as 4 seperate ones and joined them together Bet you can't tell.
These pictures are created by this suprisingly simple iterative function.
The Mandelbrot set is defined as those values of c which do not tend to infinity. It can be shown that if at any stage the modulus of z is greater then 2 then each successive iteration will have a larger modulus than the previous one and the sequence will quickly diverge to infinity.
To find what colour a point in the pic is, the complex number representing the coordinates of that point is put in the formula as c. The successive values of the function are calculated. If any value has a modulus (size) greater than 2, that point is not in the Mandelbrot set. The colour is chosen from how many iterations were completed before the modulus was greater than 2. If, after many, often thousands of iterations the programmes gives up and colours the point black (white on one or two pics). This method doesn't prove that the black points are actually in the set it just shows that the coloured one are not.
This pic covers the area between -0.10252345 and -0.10252335 horizontally and 0.89247180i and 0.89247170i vertically. It took my poorly little Amiga 1839 minutes. That's over 30 hours. I think it was worth it though, it is the best picture I have done. The reason it took so long is because I have zoomed in so much, it has to do many thousand iterations to decide whether or not a point should be black. I can't imagine that working to 15 decimal places helps either.
This pic is very similar to the above one. It's measures -0.1025234590 to -0.102523310 along the bottom and 0.892471880i to 0.892471700i upwards. I have just zoomed out a bit and recoloured it. They are both really good pics so I put them both in. This one took it 1219 mins.
This pic contains every point that is actually in the Mandelbrot set. If a point in the picture is coloured black, then the complex number corresponding to that point is in the set.Similarly, if the point is white, then the corresponding complex number is not in the set. The line of real numbers is also the line of symmetry through the middle.
One of the most amazing features of the Mandelbrot set if that an image of the entire set appears an infinite amount of times at various scales and orientations. One can be seen here also in pics 2 and 3. The region covered by this pic is -0.111 to -0.099 horizontally and 0.931i to 0.919i vertically. This pic took 249 mins to render.
Left picture: Top edge 0.957528i, Bottom edge 0.956424i, Left edge -0.102823, Right edge -0.101709. Took 120 mins.
Right picture: Top edge 0.9573i, Bottom edge 0.9570i, Left edge -0.10245, Right edge -0.10215. Took 159 mins.
The right pic a close up of the centre of the left pic.
Left: Top edge 0.957169262i, Bottom edge 0.957167445i, Left edge -0.102393230, Right edge -0.102391413. Took 221 mins.
Below: Top edge 0.69i, Bottom edge 0.64i, Left edge -0.40, Right edge -0.35. Took 416 mins.
Below: Top edge -0.631i, Bottom edge -0.663i, Left edge -0.495, Right edge -0.493. Took 236 mins.
Below right: Top Edge 0.951i, Bottom edge 0.85i, Left edge -0.15, Right edge -0.05.
