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P04 - Exponential mapping for deep zoom
This small example demonstrates the compatibility of
fractalshades.projection.Expmap projection
with deep zooms (perturbation theory).
import os
import typing
import numpy as np
import mpmath
import fractalshades
import fractalshades as fs
import fractalshades.models
import fractalshades.gui
import fractalshades.projection
from fractalshades.postproc import (
Postproc_batch,
Continuous_iter_pp,
DEM_normal_pp,
Fieldlines_pp,
DEM_pp,
Raw_pp,
Attr_pp,
Attr_normal_pp,
Fractal_array
)
from fractalshades.colors.layers import (
Color_layer,
Bool_layer,
Normal_map_layer,
Grey_layer,
Disp_layer,
Virtual_layer,
Blinn_lighting,
Overlay_mode
)
# Note: in batch mode, edit this line to change the base directory
try:
is_temp = False
plot_dir_obj = None
plot_dir = os.path.splitext(os.path.realpath(__file__))[0]
except NameError:
import tempfile
plot_dir_obj = tempfile.TemporaryDirectory()
plot_dir = plot_dir_obj.name
# Note: in batch mode, edit this line to change the local projection
# you may also call `plot` with a modified `batch_params` parameters
# (the latter allows to call from another module)
projection = fs.projection.Expmap(0.0, np.log(1.e20) + 0.3, orientation="vertical")
# projection = fs.projection.Expmap(np.log(1.e40), np.log(1.e50))
# projection = fs.projection.Expmap(np.log(1.e0), np.log(1.e10))
ks = 1.e-40
#projection = fs.projection.Cartesian()
batch_params = {
"projection": projection
}
#------------------------------------------------------------------------------
# Parameters - user editable
#------------------------------------------------------------------------------
plot_kwargs = {
"fractal": fractalshades.models.mandelbrot_M2.Perturbation_mandelbrot(
directory=plot_dir,
),
"calc_name": "std_zooming_calc",
"_1": "Zoom parameters",
"x": "-0.18476527944640054234980108927",
"y": "1.0532419344392547587734377701",
"dx": "7.603772829116657e-20",
"dps": 31,
"xy_ratio": 1.6666,
"theta_deg": 0.0,
"nx": 2400, # 2400 x 325
"_2": "Calculation parameters",
"max_iter": 500000,
"M_divergence": 1000.0,
"interior_detect": True,
"epsilon_stationnary": 0.01,
"calc_dzndc": True,
"_4": "Plotting parameters: base field",
"base_layer": "continuous_iter",
"colormap": fs.colors.cmap_register["classic"],
"cmap_func": fractalshades.numpy_utils.expr_parser.Numpy_expr(
variables=[
"x",
],
expr="np.log(x)",
),
"zmin": 0.0,
"zmax": 1.0,
"zshift": 0.05,
"mask_color": (
0.1,
0.1,
0.1,
1.0,
),
"_5": "Plotting parameters: shading",
"has_shading": False,
"shading_kind": "potential",
"lighting": fs.colors.layers.Blinn_lighting(
k_ambient=0.4,
color_ambient=[1., 1., 1.],
ls0={
'k_diffuse': 1.8,
'k_specular': 15.0,
'shininess': 500.0,
'polar_angle': 50.0,
'azimuth_angle': 20.0,
'color': [1. , 1. , 0.95],
'material_specular_color': None
},
),
"max_slope": 60.0,
"_6": "Plotting parameters: field lines",
"has_fieldlines": True,
"fieldlines_func": fractalshades.numpy_utils.expr_parser.Numpy_expr(
variables=[
"x",
],
expr="x",
),
"fieldlines_kind": "twin",
"fieldlines_zmin": -1.0,
"fieldlines_zmax": 1.0,
"backshift": 14,
"n_iter": 10,
"swirl": 0.0,
"damping_ratio": 0.8,
"twin_intensity": 0.25,
"_8": "High-quality rendering options",
"final_render": False,
"supersampling": "3x3",
"jitter": False,
"recovery_mode": False,
"_9": "Extra outputs",
"output_masks": False,
"output_normals": False,
"output_heightmaps": False,
"hmap_mask": 0.0,
"int_hmap_mask": 0.0,
"_10": "General settings",
"log_verbosity": "debug @ console + log",
"enable_multithreading": True,
"inspect_calc": False,
"no_newton": True,
"postproc_dtype": "float32",
"compute_newton": False,
"_3": None,
"max_order": None,
"max_newton": None,
"eps_newton_cv": None,
"_7": None,
"int_layer": None,
"colormap_int": None,
"cmap_func_int": None,
"zmin_int": None,
"zmax_int": None,
"lighting_int": None,
"_1b": None,
"has_skew": False,
"skew_00": 1.0,
"skew_01": 0.0,
"skew_10": 0.0,
"skew_11": 1.0,
}
#------------------------------------------------------------------------------
# Function - /!\ do not modify this section
#------------------------------------------------------------------------------
def plot(
fractal: fs.Fractal= fractalshades.models.mandelbrot_M2.Perturbation_mandelbrot(
directory=plot_dir,
),
calc_name: str="std_zooming_calc",
_1: fs.gui.collapsible_separator="Zoom parameters",
x : mpmath.mpf = "0.0",
y : mpmath.mpf = "0.0",
dx : mpmath.mpf = "10.0",
dps: int = 16,
xy_ratio: float = 1.0,
theta_deg: float = 0.0,
nx: int = 600,
_1b: fs.gui.collapsible_separator = None,
has_skew: bool = False,
skew_00: float = 1.0,
skew_01: float = 0.0,
skew_10: float = 0.0,
skew_11: float = 1.0,
_2: fs.gui.collapsible_separator="Calculation parameters",
max_iter: int = 5000,
M_divergence: float = 1000.,
interior_detect: bool = True,
epsilon_stationnary: float = 0.001,
calc_dzndc: bool = True,
_3: fs.gui.collapsible_separator = None,
compute_newton: bool = False,
max_order: int = None,
max_newton: int = None,
eps_newton_cv: float = None,
_4: fs.gui.collapsible_separator="Plotting parameters: base field",
base_layer: typing.Literal[
"continuous_iter",
"distance_estimation"
]="continuous_iter",
colormap: fs.colors.Fractal_colormap=(
fs.colors.cmap_register["classic"]
),
cmap_func: fs.numpy_utils.Numpy_expr = (
fs.numpy_utils.Numpy_expr("x", "np.log(x)")
),
zmin: float = 0.0,
zmax: float = 5.0,
zshift: float = -1.0,
mask_color: fs.colors.Color=(0.1, 0.1, 0.1, 1.0),
_7: fs.gui.collapsible_separator= None,
int_layer: typing.Literal[
"attractivity", "order", "attr / order"
]= None,
colormap_int: fs.colors.Fractal_colormap = None,
cmap_func_int: fs.numpy_utils.Numpy_expr = None,
zmin_int: float = None,
zmax_int: float = None,
_5: fs.gui.collapsible_separator = "Plotting parameters: shading",
has_shading: bool = True,
shading_kind: typing.Literal["potential"] = "potential",
lighting: Blinn_lighting = (
fs.colors.lighting_register["glossy"]
),
lighting_int: Blinn_lighting = None,
max_slope: float = 60.,
_6: fs.gui.collapsible_separator = "Plotting parameters: field lines",
has_fieldlines: bool = False,
fieldlines_func: fs.numpy_utils.Numpy_expr = (
fs.numpy_utils.Numpy_expr("x", "x")
),
fieldlines_kind: typing.Literal["overlay", "twin"] = "overlay",
fieldlines_zmin: float = -1.0,
fieldlines_zmax: float = 1.0,
backshift: int = 3,
n_iter: int = 4,
swirl: float = 0.,
damping_ratio: float = 0.8,
twin_intensity: float = 0.1,
_8: fs.gui.collapsible_separator="High-quality rendering options",
final_render: bool=False,
supersampling: fs.core.supersampling_type = "None",
jitter: bool = False,
recovery_mode: bool = False,
_9: fs.gui.collapsible_separator="Extra outputs",
output_masks: bool = False,
output_normals: bool = False,
output_heightmaps: bool = False,
hmap_mask: float = 0.,
int_hmap_mask: float = 0.,
_10: fs.gui.collapsible_separator="General settings",
log_verbosity: typing.Literal[fs.log.verbosity_enum
] = "debug @ console + log",
enable_multithreading: bool = True,
inspect_calc: bool = False,
no_newton: bool = False,
postproc_dtype: typing.Literal["float32", "float64"] = "float32",
batch_params=batch_params
):
fs.settings.log_directory = os.path.join(fractal.directory, "log")
fs.set_log_handlers(verbosity=log_verbosity)
fs.settings.enable_multithreading = enable_multithreading
fs.settings.inspect_calc = inspect_calc
fs.settings.no_newton = no_newton
fs.settings.postproc_dtype = postproc_dtype
zoom_kwargs = {
"x": x,
"y": y,
"dx": dx,
"nx": nx,
"xy_ratio": xy_ratio,
"theta_deg": theta_deg,
"has_skew": has_skew,
"skew_00": skew_00,
"skew_01": skew_01,
"skew_10": skew_10,
"skew_11": skew_11,
"projection": batch_params.get(
"projection", fs.projection.Cartesian()
)
}
if fractal.implements_deepzoom:
zoom_kwargs["precision"] = dps
fractal.zoom(**zoom_kwargs)
calc_std_div_kw = {
"calc_name": calc_name,
"subset": None,
"max_iter": max_iter,
"M_divergence": M_divergence,
# "BLA_eps": None # 1.e-6,
}
if fractal.implements_dzndc == "user":
calc_std_div_kw["calc_dzndc"] = calc_dzndc
if shading_kind == "Milnor":
calc_std_div_kw["calc_d2zndc2"] = True
if has_fieldlines:
calc_orbit = (backshift > 0)
calc_std_div_kw["calc_orbit"] = calc_orbit
calc_std_div_kw["backshift"] = backshift
if fractal.implements_interior_detection == "always":
calc_std_div_kw["epsilon_stationnary"] = epsilon_stationnary
elif fractal.implements_interior_detection == "user":
calc_std_div_kw["interior_detect"] = interior_detect
calc_std_div_kw["epsilon_stationnary"] = epsilon_stationnary
fractal.calc_std_div(**calc_std_div_kw)
# Run the calculation for the interior points - if wanted
if compute_newton:
interior = Fractal_array(
fractal, calc_name, "stop_reason", func= "x != 1"
)
fractal.newton_calc(
calc_name="interior",
subset=interior,
known_orders=None,
max_order=max_order,
max_newton=max_newton,
eps_newton_cv=eps_newton_cv,
)
pp = Postproc_batch(fractal, calc_name)
if base_layer == "continuous_iter":
pp.add_postproc(base_layer, Continuous_iter_pp())
if output_heightmaps:
pp.add_postproc("base_hmap", Continuous_iter_pp())
elif base_layer == "distance_estimation":
pp.add_postproc("continuous_iter", Continuous_iter_pp())
pp.add_postproc(base_layer, DEM_pp())
if output_heightmaps:
pp.add_postproc("base_hmap", DEM_pp())
if has_fieldlines:
pp.add_postproc(
"fieldlines",
Fieldlines_pp(n_iter, swirl, damping_ratio)
)
else:
fieldlines_kind = "None"
pp.add_postproc("interior", Raw_pp("stop_reason", func="x != 1"))
if compute_newton:
pp_int = Postproc_batch(fractal, "interior")
if int_layer == "attractivity":
pp_int.add_postproc(int_layer, Attr_pp())
if output_heightmaps:
pp_int.add_postproc("interior_hmap", Attr_pp())
elif int_layer == "order":
pp_int.add_postproc(int_layer, Raw_pp("order"))
if output_heightmaps:
pp_int.add_postproc("interior_hmap", Raw_pp("order"))
elif int_layer == "attr / order":
pp_int.add_postproc(int_layer, Attr_pp(scale_by_order=True))
if output_heightmaps:
pp_int.add_postproc(
"interior_hmap", Attr_pp(scale_by_order=True)
)
# Set of unknown points
pp_int.add_postproc(
"unknown", Raw_pp("stop_reason", func="x == 0")
)
pps = [pp, pp_int]
else:
pps = pp
if has_shading:
pp.add_postproc("DEM_map", DEM_normal_pp(kind=shading_kind))
if compute_newton:
pp_int.add_postproc("attr_map", Attr_normal_pp())
plotter = fs.Fractal_plotter(
pps,
final_render=final_render,
supersampling=supersampling,
jitter=jitter,
recovery_mode=recovery_mode
)
# The mask values & curves for heighmaps
r1 = min(hmap_mask, 0.)
r2 = max(hmap_mask, 1.)
dr = r2 - r1
hmap_curve = lambda x : (np.clip(x, 0., 1.) - r1) / dr
r1 = min(int_hmap_mask, 0.)
r2 = max(int_hmap_mask, 1.)
dr = r2 - r1
int_hmap_curve = lambda x : (np.clip(x, 0., 1.) - r1) / dr
# The layers
plotter.add_layer(Bool_layer("interior", output=output_masks))
if compute_newton:
plotter.add_layer(Bool_layer("unknown", output=output_masks))
if fieldlines_kind == "twin":
plotter.add_layer(Virtual_layer(
"fieldlines", func=fieldlines_func, output=False
))
elif fieldlines_kind == "overlay":
plotter.add_layer(Grey_layer(
"fieldlines", func=fieldlines_func,
probes_z=[fieldlines_zmin, fieldlines_zmax],
output=False
))
if has_shading:
plotter.add_layer(Normal_map_layer(
"DEM_map", max_slope=max_slope, output=output_normals
))
plotter["DEM_map"].set_mask(plotter["interior"])
if compute_newton:
plotter.add_layer(Normal_map_layer(
"attr_map", max_slope=90, output=output_normals
))
if base_layer != 'continuous_iter':
plotter.add_layer(
Virtual_layer("continuous_iter", func=None, output=False)
)
plotter.add_layer(Color_layer(
base_layer,
func=cmap_func,
colormap=colormap,
probes_z=[zmin + zshift, zmax + zshift],
output=True)
)
if output_heightmaps:
plotter.add_layer(Disp_layer(
"base_hmap",
func=cmap_func,
curve=hmap_curve,
probes_z=[zmin + zshift, zmax + zshift],
output=True
))
if compute_newton:
plotter.add_layer(Color_layer(
int_layer,
func=cmap_func_int,
colormap=colormap_int,
probes_z=[zmin_int, zmax_int],
output=False))
plotter[int_layer].set_mask(plotter["unknown"],
mask_color=mask_color)
if output_heightmaps:
plotter.add_layer(Disp_layer(
"interior_hmap",
func=cmap_func,
curve=int_hmap_curve,
probes_z=[zmin_int, zmax_int],
output=True
))
plotter["interior_hmap"].set_mask(
plotter["unknown"],
mask_color=(int_hmap_mask,)
)
if fieldlines_kind == "twin":
plotter[base_layer].set_twin_field(
plotter["fieldlines"], twin_intensity
)
elif fieldlines_kind == "overlay":
overlay_mode = Overlay_mode("tint_or_shade", pegtop=1.0)
plotter[base_layer].overlay(plotter["fieldlines"], overlay_mode)
if has_shading:
plotter[base_layer].shade(plotter["DEM_map"], lighting)
if compute_newton:
plotter[int_layer].shade(plotter["attr_map"], lighting_int)
plotter["attr_map"].set_mask(plotter["unknown"],
mask_color=(0., 0., 0., 0.))
if compute_newton:
# Overlay : alpha composite with "interior" layer ie, where it is not
# masked, we take the value of the "attr" layer
overlay_mode = Overlay_mode(
"alpha_composite",
alpha_mask=plotter["interior"],
inverse_mask=True
)
plotter[base_layer].overlay(plotter[int_layer], overlay_mode=overlay_mode)
else:
plotter[base_layer].set_mask(
plotter["interior"], mask_color=mask_color
)
if output_heightmaps:
plotter["base_hmap"].set_mask(
plotter["interior"], mask_color=(hmap_mask,)
)
plotter.plot()
if __name__ == "__main__":
try:
fs.utils.exec_no_output(plot, **plot_kwargs, batch_params=batch_params)
finally:
if plot_dir_obj is not None:
plot_dir_obj.cleanup()
Total running time of the script: ( 0 minutes 6.725 seconds)