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The dependency parking_lot needs to be updated to the latest version (0.12) to successfully compile rust-fractal-gui since rust-fractal/rust-fractal-gui#3 was merged.

• If a root is found in the series approximation, it may be better to shift the main reference to the root which will reduce the amount of glitches that need correcting in the image.
• It may be better to place the series approximation probe points on or near found roots as to reduce overskipping and reduce the amount of probes required.

Sometimes with the new glitch correction algorithm, some arrays are accessed out of bounds. This need to be investigated.

Currently, the mantexp library is not very good. This will need to be revised into a full extended float library, with optimizations for complex numbers.

One such optimization is that a complex number can be represented with a common exponent, provided the real and imaginary parts are close enough to each other. This will simplify and optimize the current code.

https://github.com/jackyarndley/rust-fractal/blob/4d5335991f06f5a49d52e97d5153e6339eef33b1/src/util/float_extended.rs#L26

I think the only time it is not safe to use frexp is for special values like 0, inf, nan. Though the range check may be a small optimization, if it took negative mantissa into account?

The current palette algorithm is hardcoded and therefore a new system should be implemented to allow for custom user defined palettes.

The series approximation can calculate the coefficients correctly, however it cannot at the moment choose the correct number of iterations to skip. There are a few automated checks to implement here.

Series approximation methods allow for a dramatic speedup particularly on deep zoom levels. In order for them to be implemented there will need to be a floatexp class containing a floating point number as well as an integer exponent.

In order to reuse the reference some of the program has to be reorganized:

• Make reference iteration and series approximation separate
• Glitch correction requires the current z value in high precision, at the series approximation limit. This can use a lot of memory. A better option might be to only store every thousandth iteration of the reference in high precision, and iterate from here for each glitch reference.

Cargo does not successfully build on current Mac OS (Ventura 13.0).
I have found the workaround:

• Here is my Cargo.toml (remember to remove the .txt in the filename). In particular rug and gmp-mpfr-sys need to have updated versions to build successfully.

Usage hint:

• Once cargo build --release finishes, in the git repo folder (where Cargo.toml lives), remember to mkdir output (otherwise program will panic and quit) and then try running ./target/release/main -o default.toml locations/flake.toml

Cargo.toml.txt

The current algorithm checks the approximation every iteration. It would be possible to check only once every 100 iterations and back step when the approximation is no longer valid.