About Claude's post on the old forum:

http://www.fractalforums.com/index.php?topic=25458.msg103793#msg103793An example might help: say you are using reference c0 and there is a glitch at iteration 12345, then the new reference c1 at the semantic center of the glitch (where z = 0, a minibrot nucleus) has period 12345 and has z = 0 at iteration 0, 12345, 24690, ... As we are at iteration 12345, we can just adjust the delta c values by (c1 - c0), and leave the delta z values the same- they are near 0 (we found a glitch, remember) and surrounding the new reference c1 which has its z 12345 at 0. By periodicity, we don't need to restart the iterations of the reference, its z is 0 after 12345 iterations anyway. So split the glitched pixels out into a separate batch with the new reference, the old reference is still used for the non-glitched pixels. So the glitch correction happens at the same time as rendering, no separate passes afterwards.

Before asking questions, here's my notation: \( X_n(c_i) \) is the high precision (reference) orbit of point \( c_i \), \( z_n(c) \) is the actual computed native precision PT orbit of \( c \), \( w_n(\delta) \) is the perturbation in low precision s.t. \( z_n(c) = w_n(\delta) + X_n(c_i) \) for reference point \( c_i \), and \( c = c_i + \delta \).

We start with reference \( c_0 \) until we detect an error ("glitch") in \( w \) at a \( \delta_1 \) corresponding to \( c_1 = c_0 + \delta_1 \) at iteration N=12345. Using Pauldelbrot's criterium we have at the glitch \( |z_n(c1)/X_n(c0)|<tol\approx 10^{-3} \).

We then promote \( c_1 \) (actually a point close to it, call it \( c_1^* \)) to a reference point by searching around it for a mini with period N, and compute its orbit from N on in full precision, starting at 0.

**Question:** do you always find this mini? As we have an "error" in \( w_n \) should we not distrust what it tells us (period is N)? Esp. since the condition is only triggered after \( w \) gets big, and the \( \delta \) term has dropped out a while ago already.

Then a new reference orbit \( X_n(c_1^*) \) computed from N on is used for "the glitched pixels".

**Question:** are those the pixels that glitched at the same iteration N that \( w_N(\delta_1) \) glitched?

If so, would it not be better to "hand over" more pixels that may glitch later on to \( c_1^* \), by dividing all the pixels according to whether the are closer to \( c_0 \) or \( c_1 \) using the distance metric \( d(c_1,c_2)=|z_n(c1)-z_n(c_2)| \)?

Finally, could you get away with saying at iteration N we discovered another period mini with period N, just use \( c_1 \) as new reference point, and set \( X_n(c1) = z_n(c_1) \) for \( n<N \), and \( X_N(c_1) = 0 \) (was small) and simply reuse this sequence without recomputing anything? I think not, but am not sure why.

Hope those are not too many question but I intend to implement this, and it's better to figure out things before coding, rather than after.

If you could point me to the right files on mathr.com where this is implemented that would help too. I searched but got lost...