Streamline Plots in Python
How to make a streamline plot in Python. A streamline plot displays vector field data.
New to Plotly?
Plotly is a free and open-source graphing library for Python. We recommend you read our Getting Started guide for the latest installation or upgrade instructions, then move on to our Plotly Fundamentals tutorials or dive straight in to some Basic Charts tutorials.
A Streamline plot is a representation based on a 2-D vector field interpreted as a velocity field, consisting of closed curves tangent to the velocity field. In the case of a stationary velocity field, streamlines coincide with trajectories (see also the Wikipedia page on streamlines, streaklines and pathlines).
For the streamline figure factory, one needs to provide
- uniformly spaced ranges of
x
andy
values (1D) - 2-D velocity values
u
andv
defined on the cross-product (np.meshgrid(x, y)
) ofx
andy
.
Velocity values are interpolated when determining the streamlines. Streamlines are initialized on the boundary of the x-y
domain.
Basic Streamline Plot¶
Streamline plots can be made with a figure factory as detailed in this page.
import plotly.figure_factory as ff
import numpy as np
x = np.linspace(-3, 3, 100)
y = np.linspace(-3, 3, 100)
Y, X = np.meshgrid(x, y)
u = -1 - X**2 + Y
v = 1 + X - Y**2
# Create streamline figure
fig = ff.create_streamline(x, y, u, v, arrow_scale=.1)
fig.show()
Streamline and Source Point Plot¶
import plotly.figure_factory as ff
import plotly.graph_objects as go
import numpy as np
N = 50
x_start, x_end = -2.0, 2.0
y_start, y_end = -1.0, 1.0
x = np.linspace(x_start, x_end, N)
y = np.linspace(y_start, y_end, N)
X, Y = np.meshgrid(x, y)
source_strength = 5.0
x_source, y_source = -1.0, 0.0
# Compute the velocity field on the mesh grid
u = (source_strength/(2*np.pi) *
(X - x_source)/((X - x_source)**2 + (Y - y_source)**2))
v = (source_strength/(2*np.pi) *
(Y - y_source)/((X - x_source)**2 + (Y - y_source)**2))
# Create streamline figure
fig = ff.create_streamline(x, y, u, v,
name='streamline')
# Add source point
fig.add_trace(go.Scatter(x=[x_source], y=[y_source],
mode='markers',
marker_size=14,
name='source point'))
fig.show()
See also¶
For a 3D version of streamlines, use the trace go.Streamtube
documented here.
For representing the 2-D vector field as arrows, see the quiver plot tutorial.
Reference¶
For more info on ff.create_streamline()
, see the full function reference
What About Dash?¶
Dash is an open-source framework for building analytical applications, with no Javascript required, and it is tightly integrated with the Plotly graphing library.
Learn about how to install Dash at https://dash.plot.ly/installation.
Everywhere in this page that you see fig.show()
, you can display the same figure in a Dash application by passing it to the figure
argument of the Graph
component from the built-in dash_core_components
package like this:
import plotly.graph_objects as go # or plotly.express as px
fig = go.Figure() # or any Plotly Express function e.g. px.bar(...)
# fig.add_trace( ... )
# fig.update_layout( ... )
from dash import Dash, dcc, html
app = Dash()
app.layout = html.Div([
dcc.Graph(figure=fig)
])
app.run_server(debug=True, use_reloader=False) # Turn off reloader if inside Jupyter