.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/misc/plot_perlin_noise.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_misc_plot_perlin_noise.py: Vector Field Generative Art with Perlin noise ============================================= Hello world .. GENERATED FROM PYTHON SOURCE LINES 8-33 .. code-block:: default import numpy as np import pandas as pd import matplotlib.pyplot as plt import seaborn as sns from noise import pnoise2 octaves = 5 factor = 3.0 num_lines = 600 num_steps = 50 step_sizes = 0.5 * (np.arange(10) + 1.0) seed = 42 # set random seed for reproducibility random_state = np.random.RandomState(seed) # resolution h, w = 200, 200 y, x = np.ogrid[:h, :w] X, Y = np.broadcast_arrays(x, y) .. GENERATED FROM PYTHON SOURCE LINES 35-39 The function ``pnoise2`` has range [-1, 1]. However, the outputs tend mostly to be centered around 0. Let's blow up the range by some ``factor`` and squash it through the :math:`\tanh` function so that it is still in the desired range. .. GENERATED FROM PYTHON SOURCE LINES 39-42 .. code-block:: default Z = np.tanh(factor * np.vectorize(pnoise2)(x/w, y/h, octaves=octaves)) # range [-1, 1] theta = np.pi * Z # range [-pi, pi] .. GENERATED FROM PYTHON SOURCE LINES 43-44 Sparsify the grid so we can later draw intelligible quiver plots. .. GENERATED FROM PYTHON SOURCE LINES 44-54 .. code-block:: default w_factor = h_factor = 10 x_sparse = x[..., ::w_factor] y_sparse = y[::h_factor] X_sparse = X[::h_factor, ::w_factor] Y_sparse = Y[::h_factor, ::w_factor] theta_sparse = theta[::w_factor, ::w_factor] .. GENERATED FROM PYTHON SOURCE LINES 55-56 We use use Perlin noise at every grid point as the angle (in radians). .. GENERATED FROM PYTHON SOURCE LINES 56-68 .. code-block:: default fig, ax = plt.subplots(figsize=(10, 8)) ax.set_title(r"angle $\theta$ (rad)") contours = ax.pcolormesh(X, Y, theta, cmap="twilight") fig.colorbar(contours, ax=ax) ax.set_xlabel(r"$x$") ax.set_ylabel(r"$y$") plt.show() .. image:: /auto_examples/misc/images/sphx_glr_plot_perlin_noise_001.png :alt: angle $\theta$ (rad) :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none /usr/src/app/examples/misc/plot_perlin_noise.py:60: MatplotlibDeprecationWarning: shading='flat' when X and Y have the same dimensions as C is deprecated since 3.3. Either specify the corners of the quadrilaterals with X and Y, or pass shading='auto', 'nearest' or 'gouraud', or set rcParams['pcolor.shading']. This will become an error two minor releases later. contours = ax.pcolormesh(X, Y, theta, cmap="twilight") .. GENERATED FROM PYTHON SOURCE LINES 69-71 For sanity-check, we view the numerical values of the angles normalized by :math:`\pi` on the heatmap. .. GENERATED FROM PYTHON SOURCE LINES 71-75 .. code-block:: default data = pd.DataFrame(theta_sparse / np.pi, index=y_sparse.squeeze(axis=1), columns=x_sparse.squeeze(axis=0)) .. GENERATED FROM PYTHON SOURCE LINES 76-88 .. code-block:: default fig, ax = plt.subplots(figsize=(10, 8)) ax.set_title(r"angle $\theta / \pi$ (rad)") sns.heatmap(data, annot=True, fmt=".2f", cmap="twilight", ax=ax) ax.invert_yaxis() ax.set_xlabel(r"$x$") ax.set_ylabel(r"$y$") plt.show() .. image:: /auto_examples/misc/images/sphx_glr_plot_perlin_noise_002.png :alt: angle $\theta / \pi$ (rad) :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 89-91 Flow field ---------- .. GENERATED FROM PYTHON SOURCE LINES 91-94 .. code-block:: default dx = np.cos(theta_sparse) dy = np.sin(theta_sparse) .. GENERATED FROM PYTHON SOURCE LINES 95-105 .. code-block:: default fig, ax = plt.subplots(figsize=(10, 8)) ax.quiver(x_sparse, y_sparse, dx, dy) ax.set_xlabel(r"$x$") ax.set_ylabel(r"$y$") plt.show() .. image:: /auto_examples/misc/images/sphx_glr_plot_perlin_noise_003.png :alt: plot perlin noise :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 106-108 Path ---- .. GENERATED FROM PYTHON SOURCE LINES 108-129 .. code-block:: default # TODO: `w`, `h` arguments def line(x, y, x_lim, y_lim, step_fn, num_steps, step_size=1.0): x_min, x_max = x_lim y_min, y_max = y_lim if not (num_steps and x_min <= x < x_max and y_min <= y < y_max): return [], [] dx, dy = step_fn(x, y, step_size=step_size) xs, ys = line(x=x+dx, y=y+dy, x_lim=x_lim, y_lim=y_lim, step_fn=step_fn, num_steps=num_steps-1, step_size=step_size) xs.append(x) ys.append(y) return xs, ys .. GENERATED FROM PYTHON SOURCE LINES 130-140 .. code-block:: default def step(x, y, step_size): j, i = int(x), int(y) dx = step_size * np.cos(theta[i, j]) dy = step_size * np.sin(theta[i, j]) return dx, dy .. GENERATED FROM PYTHON SOURCE LINES 141-148 .. code-block:: default x = y = 25 xs, ys = line(x, y, x_lim=(0, w), y_lim=(0, h), step_fn=step, num_steps=num_steps, step_size=5.0) _xs = np.asarray(xs[::-1]) _ys = np.asarray(ys[::-1]) .. GENERATED FROM PYTHON SOURCE LINES 149-160 .. code-block:: default fig, ax = plt.subplots(figsize=(10, 8)) ax.quiver(_xs[:-1], _ys[:-1], _xs[1:] - _xs[:-1], _ys[1:] - _ys[:-1], scale_units='xy', angles='xy', scale=1.0, width=3e-3, color='r') ax.quiver(x_sparse, y_sparse, dx, dy) ax.set_xlabel(r"$x$") ax.set_ylabel(r"$y$") plt.show() .. image:: /auto_examples/misc/images/sphx_glr_plot_perlin_noise_004.png :alt: plot perlin noise :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 161-177 .. code-block:: default dfs = [] for step_size in step_sizes: for lineno in range(num_lines): # sample starting point uniformly at random x = w * random_state.rand() y = h * random_state.rand() xs, ys = line(x, y, x_lim=(0, w), y_lim=(0, h), step_fn=step, num_steps=num_steps, step_size=step_size) df = pd.DataFrame(dict(lineno=lineno, stepsize=step_size, x=xs, y=ys)) dfs.append(df) .. GENERATED FROM PYTHON SOURCE LINES 178-181 .. code-block:: default data = pd.concat(dfs, axis="index", sort=True) data .. raw:: html
lineno stepsize x y
0 0 0.5 99.311017 188.221356
1 0 0.5 98.811904 188.251132
2 0 0.5 98.312791 188.280909
3 0 0.5 97.813378 188.305127
4 0 0.5 97.313965 188.329345
... ... ... ... ...
5 599 5.0 183.639697 44.095758
6 599 5.0 183.508302 49.094031
7 599 5.0 184.229680 54.041719
8 599 5.0 185.655844 58.834010
9 599 5.0 187.717772 63.389058

215921 rows × 4 columns



.. GENERATED FROM PYTHON SOURCE LINES 182-192 .. code-block:: default fig, ax = plt.subplots(figsize=(10, 8)) sns.lineplot(x='x', y='y', hue='stepsize', units='lineno', estimator=None, sort=False, palette='Spectral', legend=None, linewidth=1.0, alpha=0.4, data=data, ax=ax) ax.set_xlabel(r"$x$") ax.set_ylabel(r"$y$") plt.show() .. image:: /auto_examples/misc/images/sphx_glr_plot_perlin_noise_005.png :alt: plot perlin noise :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 38.293 seconds) .. _sphx_glr_download_auto_examples_misc_plot_perlin_noise.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_perlin_noise.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_perlin_noise.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_