Fractals/Fractalshades

Fractalshades by Geoffroy Billotey instalation pip install pip setuptools --upgrade pip install fractalshades Where ? zalman:~$ pip list -v Package Version Location Installer ----------------------- --------------- ------------------------------------------- --------- apturl 0.5.2 /usr/lib/python3/dist-packages bcrypt 3.2.0 /usr/lib/python3/dist-packages blinker 1.4 /usr/lib/python3/dist-packages Brlapi 0.8.3 /usr/lib/python3/dist-packages certifi 2020.6.20 /usr/lib/python3/dist-packages chardet 4.0.0 /usr/lib/python3/dist-packages chrome-gnome-shell 0.0.0 /usr/lib/python3/dist-packages click 8.0.3 /usr/lib/python3/dist-packages colorama 0.4.4 /usr/lib/python3/dist-packages command-not-found 0.3 /usr/lib/python3/dist-packages cryptography 3.4.8 /usr/lib/python3/dist-packages cupshelpers 1.0 /usr/lib/python3/dist-packages dbus-python 1.2.18 /usr/lib/python3/dist-packages defer 1.0.6 /usr/lib/python3/dist-packages Deprecated 1.2.13 /usr/lib/python3/dist-packages distro 1.7.0 /usr/lib/python3/dist-packages distro-info 1.1build1 /usr/lib/python3/dist-packages duplicity 0.8.21 /usr/lib/python3/dist-packages fasteners 0.14.1 /usr/lib/python3/dist-packages fractalshades 0.5.6 /home/a/.local/lib/python3.10/site-packages pip For interactive exploration, a GUI is implemented under PyQt6. Projections A Projection defines a mapping acting on the screen-pixels before iteration. Projections doc file projections.py exponential An exponential projection will map : as follows: where: The `xy_ratio` of the zoom will be adjusted (during run time) to ensure that: extends from to def adjust_to_zoom(self, fractal): # We need to adjust the fractal xy_ratio in order to match hmax - hmin # target: dh = 2. * np.pi * xy_ratio if self.premul_1j: xy_ratio = (np.pi * 2.) / self.dh nx = int(fractal.nx * xy_ratio + 0.5) else: xy_ratio = self.dh / (np.pi * 2.) nx = fractal.nx fractal.xy_ratio = self.xy_ratio = xy_ratio fractal.zoom_kwargs["xy_ratio"] = xy_ratio fractal.nx = nx fractal.zoom_kwargs["nx"] = nx logger.info( "Adjusted parameters for Expmap projection:\n" f"zoom parameter nx: {fractal.nx}\n" f"zoom parameter xy_ratio: {fractal.xy_ratio}" ) self.make_impl() This class can be used with arbitrary-precision deep zooms. Parameters hmin: str or float or mpmath.mpf scaling at the lower end of the x-axis hmax: str or float or mpmath.mpf scaling at the higher end of the x-axis rotates_df: bool. If ``True``, the derivative will be scaled but also rotated according to the mapping. Otherwise, only the scaling will be taken into account. A rule of thumb is this value shall be set to ``True`` for a standalone picture, and to ``False`` if used as input for a movie making tool It is defined in class class Expmap(Projection): def __init__(self, hmin, hmax, rotates_df=True, orientation="horizontal"): Examples P01-feigenbaum_expmap.html P04-deep_expmap projection = fs.projection.Expmap(-1.3, np.log(1.e7) + 0.3) so hmin = -1.3 hmax = log(1.e7) + 0.3 = 10000000.3 A simple pass-through Frame, extracting the raw my_db data is: fractalshades.db.Frame( x=0., y=0., dx=1.0, nx=my_db.zoom_kwargs["nx"], xy_ratio=my_db.zoom_kwargs["xy_ratio"] ) References