.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/projections/P02-inversion.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_examples_projections_P02-inversion.py: ======================================================== P02 - Inversion of the Mandelbrot set ======================================================== This example demonstrates a basic use of the class `Generic_mapping`. The following mapping is applied: .. math:: f(z) = \frac{1}{z} Reference: `fractalshades.projection.Generic_mapping` .. GENERATED FROM PYTHON SOURCE LINES 18-614 .. image-sg:: /examples/projections/images/sphx_glr_P02-inversion_001.png :alt: P02 inversion :srcset: /examples/projections/images/sphx_glr_P02-inversion_001.png :class: sphx-glr-single-img .. code-block:: default import os import typing import numpy as np import mpmath from PyQt6 import QtGui import numba import fractalshades import fractalshades as fs import fractalshades.models as fsm import fractalshades.gui as fsgui import fractalshades.colors as fscolors 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 ) x = 1. y = 0. dx = 8. xy_ratio = 1.6 @numba.njit def f(z): # define the inversion function return 1 / z @numba.njit def df(z): # differential: used to correctly implement shading return -1. / z ** 2 projection = fs.projection.Generic_mapping(f, df) batch_params = { "projection": projection } #------------------------------------------------------------------------------ # Parameters - user editable #------------------------------------------------------------------------------ plot_kwargs = { "fractal": None, "calc_name": "std_zooming_calc", "_1": "Zoom parameters", "x": x, "y": y, "dx": dx, "xy_ratio": xy_ratio, "theta_deg": 0.0, "nx": 2400, "_2": "Calculation parameters", "max_iter": 5000, "M_divergence": 1000.0, "epsilon_stationnary": 0.01, "_3": "Newton parameters", "compute_newton": True, "max_order": 30000, "max_newton": 20, "eps_newton_cv": 1e-08, "_4": "Plotting parameters: base field", "base_layer": "continuous_iter", "colormap": fs.colors.Fractal_colormap( colors=[[0.67450982, 0.67450982, 0.67450982], [0.67450982, 0.67450982, 0.67450982]], kinds=['Lch'], grad_npts=[3], grad_funcs=['x'], extent='repeat' ), "cmap_func": fractalshades.numpy_utils.expr_parser.Numpy_expr( variables=[ "x", ], expr="np.log(x)", ), "zmin": 0.0, "zmax": 5.0, "zshift": -1.0, "mask_color": ( 0.1, 0.1, 0.1, 1.0, ), "_7": "Plotting parameters: Newton field", "int_layer": "attractivity", "colormap_int": fs.colors.Fractal_colormap( colors=[[0. , 0. , 0. ], [0.4823 , 0.8392 , 0.8549 ]], kinds=['Lch'], grad_npts=[8], grad_funcs=['x**2'], extent='mirror' ), "cmap_func_int": fractalshades.numpy_utils.expr_parser.Numpy_expr( variables=[ "x", ], expr="x", ), "zmin_int": 0.0, "zmax_int": 1.0, "_5": "Plotting parameters: shading", "has_shading": True, "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': 135.0, 'azimuth_angle': 20.0, 'color': [1. , 1. , 0.95], 'material_specular_color': None }, ), "lighting_int": 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': 135.0, 'azimuth_angle': 20.0, 'color': [1. , 1. , 0.95], 'material_specular_color': None }, ), "max_slope": 60.0, "_6": "Plotting parameters: field lines", "has_fieldlines": False, "fieldlines_func": fractalshades.numpy_utils.expr_parser.Numpy_expr( variables=[ "x", ], expr="x", ), "fieldlines_kind": "overlay", "fieldlines_zmin": -1.0, "fieldlines_zmax": 1.0, "backshift": 3, "n_iter": 4, "swirl": 0.0, "damping_ratio": 0.8, "twin_intensity": 0.1, "_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": False, "postproc_dtype": "float32", "_1b": None, "has_skew": False, "skew_00": 1.0, "skew_01": 0.0, "skew_10": 0.0, "skew_11": 1.0, "calc_dzndc": False, "interior_detect": True, "dps": None, } #------------------------------------------------------------------------------ # Function - /!\ do not modify this section #------------------------------------------------------------------------------ def plot( fractal: fs.Fractal=None, calc_name: str="std_zooming_calc", _1: fs.gui.collapsible_separator="Zoom parameters", x: float = 0.0, y: float = 0.0, dx: float = 10.0, dps: int = None, 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 = False, _3: fs.gui.collapsible_separator = "Newton parameters", compute_newton: bool = True, max_order: int = 1500, max_newton: int = 20, eps_newton_cv: float =1.e-8, _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="Plotting parameters: Newton field", int_layer: typing.Literal[ "attractivity", "order", "attr / order" ]="attractivity", colormap_int: fs.colors.Fractal_colormap = ( fs.colors.cmap_register["classic"] ), cmap_func_int: fs.numpy_utils.Numpy_expr = ( fs.numpy_utils.Numpy_expr("x", "x") ), zmin_int: float = 0.0, zmax_int: float = 1.0, _5: fs.gui.collapsible_separator = "Plotting parameters: shading", has_shading: bool = True, shading_kind : typing.Literal["potential", "Milnor"] = "potential", lighting: Blinn_lighting = ( fs.colors.lighting_register["glossy"] ), lighting_int: Blinn_lighting = ( fs.colors.lighting_register["glossy"] ), 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={} ): 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, } 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__": # Some magic to get the directory for plotting: with a name that matches # the file or a temporary dir if we are building the documentation try: realpath = os.path.realpath(__file__) plot_dir = os.path.splitext(realpath)[0] plot_kwargs["fractal"] = fs.models.mandelbrot_M2.Mandelbrot( directory=plot_dir, ) plot(**plot_kwargs, batch_params=batch_params) except NameError: import tempfile with tempfile.TemporaryDirectory() as plot_dir: plot_kwargs["fractal"] = fs.models.mandelbrot_M2.Mandelbrot( directory=plot_dir ) fs.utils.exec_no_output( plot, **plot_kwargs, batch_params=batch_params ) .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 8.471 seconds) .. _sphx_glr_download_examples_projections_P02-inversion.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: P02-inversion.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: P02-inversion.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_