.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/04_demos/viz_brownian_motion.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_04_demos_viz_brownian_motion.py: ====================================================================== Brownian motion ====================================================================== Brownian motion, or pedesis, is the random motion of particles suspended in a medium. In this animation, path followed by 20 particles exhibiting brownian motion in 3D is plotted. Importing necessary modules .. GENERATED FROM PYTHON SOURCE LINES 11-17 .. code-block:: default import numpy as np from scipy.stats import norm from fury import actor, ui, utils, window .. GENERATED FROM PYTHON SOURCE LINES 18-37 Let's define some variable and their description: * **total_time**: time to be discretized via time_steps (default: 5) * **num_total_steps**: total number of steps each particle will take (default: 300) * **time_step**: By default, it is equal to total_time / num_total_steps * **counter_step**: to keep track of number of steps taken (initialised to 0) * **delta**: delta determines the "speed" of the Brownian motion. Increase delta to speed up the motion of the particle(s). The random variable of the position has a normal distribution whose mean is the position at counter_step = 0 and whose variance is equal to delta**2*time_step. (default: 1.8) * **num_particles**: number of particles whose path will be plotted (default: 20) * **path_thickness**: thickness of line(s) that will be used to plot the path(s) of the particle(s) (default: 3) * **origin**: coordinate from which the the particle(s) begin the motion (default: [0, 0, 0]) .. GENERATED FROM PYTHON SOURCE LINES 37-46 .. code-block:: default total_time = 5 num_total_steps = 300 counter_step = 0 delta = 1.8 num_particles = 20 path_thickness = 3 origin = [0, 0, 0] .. GENERATED FROM PYTHON SOURCE LINES 47-49 We define a particle function that will return an actor, store and update coordinates of the particles (the path of the particles). .. GENERATED FROM PYTHON SOURCE LINES 49-74 .. code-block:: default def particle( colors, origin=[0, 0, 0], num_total_steps=300, total_time=5, delta=1.8, path_thickness=3, ): origin = np.asarray(origin, dtype=float) position = np.tile(origin, (num_total_steps, 1)) path_actor = actor.line([position], colors, linewidth=path_thickness) path_actor.position = position path_actor.delta = delta path_actor.num_total_steps = num_total_steps path_actor.time_step = total_time / num_total_steps path_actor.vertices = utils.vertices_from_actor(path_actor) path_actor.no_vertices_per_point = len(path_actor.vertices) / num_total_steps path_actor.initial_vertices = path_actor.vertices.copy() - np.repeat( position, path_actor.no_vertices_per_point, axis=0 ) return path_actor .. GENERATED FROM PYTHON SOURCE LINES 75-76 The function `update_path` will simulate the the brownian motion. .. GENERATED FROM PYTHON SOURCE LINES 76-91 .. code-block:: default def update_path(act, counter_step): if counter_step < act.num_total_steps: x, y, z = act.position[counter_step - 1] x += norm.rvs(scale=act.delta**2 * act.time_step) y += norm.rvs(scale=act.delta**2 * act.time_step) z += norm.rvs(scale=act.delta**2 * act.time_step) act.position[counter_step:] = [x, y, z] act.vertices[:] = act.initial_vertices + np.repeat( act.position, act.no_vertices_per_point, axis=0 ) utils.update_actor(act) .. GENERATED FROM PYTHON SOURCE LINES 92-93 Creating a scene object and configuring the camera's position .. GENERATED FROM PYTHON SOURCE LINES 93-105 .. code-block:: default scene = window.Scene() scene.background((1.0, 1.0, 1.0)) scene.zoom(1.7) scene.set_camera( position=(0, 0, 40), focal_point=(0.0, 0.0, 0.0), view_up=(0.0, 0.0, 0.0) ) showm = window.ShowManager( scene, size=(600, 600), reset_camera=True, order_transparent=True ) .. GENERATED FROM PYTHON SOURCE LINES 106-107 Creating a list of particle objects .. GENERATED FROM PYTHON SOURCE LINES 107-121 .. code-block:: default l_particle = [ particle( colors=np.random.rand(1, 3), origin=origin, num_total_steps=num_total_steps, total_time=total_time, path_thickness=path_thickness, ) for _ in range(num_particles) ] scene.add(*l_particle) .. GENERATED FROM PYTHON SOURCE LINES 122-123 Creating a container (cube actor) inside which the particle(s) move around .. GENERATED FROM PYTHON SOURCE LINES 123-129 .. code-block:: default container_actor = actor.box( centers=np.array([[0, 0, 0]]), colors=(0.5, 0.9, 0.7, 0.4), scales=6 ) scene.add(container_actor) .. GENERATED FROM PYTHON SOURCE LINES 130-131 Initializing text box to display the name of the animation .. GENERATED FROM PYTHON SOURCE LINES 131-137 .. code-block:: default tb = ui.TextBlock2D(bold=True, position=(235, 40), color=(0, 0, 0)) tb.message = 'Brownian Motion' scene.add(tb) .. GENERATED FROM PYTHON SOURCE LINES 138-139 The path of the particles exhibiting Brownian motion is plotted here .. GENERATED FROM PYTHON SOURCE LINES 139-152 .. code-block:: default def timer_callback(_obj, _event): global counter_step, list_particle counter_step += 1 for p in l_particle: update_path(p, counter_step=counter_step) showm.render() scene.azimuth(2) if counter_step == num_total_steps: showm.exit() .. GENERATED FROM PYTHON SOURCE LINES 153-154 Run every 30 milliseconds .. GENERATED FROM PYTHON SOURCE LINES 154-159 .. code-block:: default showm.add_timer_callback(True, 30, timer_callback) showm.start() window.record(showm.scene, size=(600, 600), out_path='viz_brownian_motion.png') .. image-sg:: /auto_examples/04_demos/images/sphx_glr_viz_brownian_motion_001.png :alt: viz brownian motion :srcset: /auto_examples/04_demos/images/sphx_glr_viz_brownian_motion_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 9.435 seconds) .. _sphx_glr_download_auto_examples_04_demos_viz_brownian_motion.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: viz_brownian_motion.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: viz_brownian_motion.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_