Fractals/Fractalshades
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< Fractals
Fractalshades by Geoffroy Billotey
instalation
[edit | edit source]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
[edit | edit source]A Projection defines a mapping acting on the screen-pixels before iteration.
Projections
- doc
- file projections.py
exponential
[edit | edit source]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
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"]
)