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This is a plotting library for use with matplotlib to make ternary plots plots in the two dimensional simplex projected onto a two dimensional plane.

The library provides functions for plotting projected lines, curves (trajectories), scatter plots, and heatmaps. There are several examples and a short tutorial below.


Last image from: Genetic Drift and Selection in Many-Allele Range Expansions.

See the citations below for more example images.

Citations and Recent Usage in Publications


Have you used python-ternary in a publication? Open a PR or issue to include your citations or example plots!

See the partial list of citations and instructions on how to cite.



You can install python-ternary with conda:

conda config --add channels conda-forge
conda install python-ternary

See here for more information.


You can install the current release (1.0.6) with pip:

    pip install python-ternary


Alternatively you can clone the repository and run in the usual manner:

    git clone [email protected]:marcharper/python-ternary.git
    cd python-ternary
    python install

Usage, Examples, Plotting Functions

You can explore some of these examples with this Jupyter notebook.

The easiest way to use python-ternary is with the wrapper class TernaryAxesSubplot, which mimics Matplotlib's AxesSubplot. Start with:

    fig, tax = ternary.figure()

With a ternary axes object tax you can use many of the usual matplotlib axes object functions:

    tax.set_title("Scatter Plot", fontsize=20)
    tax.scatter(points, marker='s', color='red', label="Red Squares")

Most drawing functions can take standard matplotlib keyword arguments such as linestyle and linewidth. You can use LaTeX in titles and labels.

If you need to act directly on the underlying matplotlib axes, you can access them easily:

    ax = tax.get_axes()

You can also wrap an existing Matplotlib AxesSubplot object:

    figure, ax = pyplot.subplots()
    tax = ternary.TernaryAxesSubplot(ax=ax)

This is useful if you want to use ternary as a part of another figure, such as

    from matplotlib import pyplot, gridspec

    gs = gridspec.GridSpec(2, 2)
    ax = pyplot.subplot(gs[0, 0])
    figure, tax = ternary.figure(ax=ax)

Some ternary functions expect the simplex to be partitioned into some number of steps, determined by the scale parameter. A few functions will do this partitioning automatically for you, but when working with real data or simulation output, you may have partitioned already. If you are working with probability distributions, just use scale=1 (the default). Otherwise the scale parameter effectively controls the resolution of many plot types (e.g. heatmaps).

TernaryAxesSubplot objects keep track of the scale, axes, and other parameters, supplying them as needed to other functions.

Simplex Boundary and Gridlines

The following code draws a boundary for the simplex and gridlines.

    import ternary

    ## Boundary and Gridlines
    scale = 40
    figure, tax = ternary.figure(scale=scale)

    # Draw Boundary and Gridlines
    tax.gridlines(color="black", multiple=5)
    tax.gridlines(color="blue", multiple=1, linewidth=0.5)

    # Set Axis labels and Title
    fontsize = 20
    tax.set_title("Simplex Boundary and Gridlines", fontsize=fontsize)
    tax.left_axis_label("Left label $\\alpha^2$", fontsize=fontsize)
    tax.right_axis_label("Right label $\\beta^2$", fontsize=fontsize)
    tax.bottom_axis_label("Bottom label $\\Gamma - \\Omega$", fontsize=fontsize)

    # Set ticks
    tax.ticks(axis='lbr', linewidth=1)

    # Remove default Matplotlib Axes

Drawing lines

You can draw individual lines between any two points with line and lines parallel to the axes with horizonal_line, left_parallel_line, and right_parallel_line:

    import ternary
    scale = 40
    figure, tax = ternary.figure(scale=scale)
    # Draw Boundary and Gridlines
    tax.gridlines(color="blue", multiple=5)
    # Set Axis labels and Title
    fontsize = 12
    offset = 0.14
    tax.set_title("Various Lines\n", fontsize=fontsize)
    tax.right_corner_label("X", fontsize=fontsize)
    tax.top_corner_label("Y", fontsize=fontsize)
    tax.left_corner_label("Z", fontsize=fontsize)
    tax.left_axis_label("Left label $\\alpha^2$", fontsize=fontsize, offset=offset)
    tax.right_axis_label("Right label $\\beta^2$", fontsize=fontsize, offset=offset)
    tax.bottom_axis_label("Bottom label $\\Gamma - \\Omega$", fontsize=fontsize, offset=offset)
    # Draw lines parallel to the axes
    tax.left_parallel_line(10, linewidth=2., color='red', linestyle="--")
    tax.right_parallel_line(20, linewidth=3., color='blue')

    # Draw an arbitrary line, ternary will project the points for you
    p1 = (22, 8, 10)
    p2 = (2, 22, 16)
    tax.line(p1, p2, linewidth=3., marker='s', color='green', linestyle=":")
    tax.ticks(axis='lbr', multiple=5, linewidth=1, offset=0.025)

The line drawing functions accept the matplotlib keyword arguments of Line2D.


Curves can be plotted by specifying the points of the curve, just like matplotlib's plot. Simply use:


Points is a list of tuples or numpy arrays, such as [(0.5, 0.25, 0.25), (1./3, 1./3, 1./3)],

    import ternary

    ## Sample trajectory plot
    figure, tax = ternary.figure(scale=1.0)
    tax.gridlines(multiple=0.2, color="black")
    tax.set_title("Plotting of sample trajectory data", fontsize=20)
    points = []
    # Load some data, tuples (x,y,z)
    with open("sample_data/curve.txt") as handle:
        for line in handle:
            points.append(list(map(float, line.split(' '))))
    # Plot the data
    tax.plot(points, linewidth=2.0, label="Curve")
    tax.ticks(axis='lbr', multiple=0.2, linewidth=1, tick_formats="%.1f")

There are many more examples in this paper.

Scatter Plots

Similarly, ternary can make scatter plots:

    import ternary

    ### Scatter Plot
    scale = 40
    figure, tax = ternary.figure(scale=scale)
    tax.set_title("Scatter Plot", fontsize=20)
    tax.gridlines(multiple=5, color="blue")
    # Plot a few different styles with a legend
    points = random_points(30, scale=scale)
    tax.scatter(points, marker='s', color='red', label="Red Squares")
    points = random_points(30, scale=scale)
    tax.scatter(points, marker='D', color='green', label="Green Diamonds")
    tax.ticks(axis='lbr', linewidth=1, multiple=5)


Ternary can plot heatmaps in two ways and three styles. Given a function, ternary will evaluate the function at the specified number of steps (determined by the scale, expected to be an integer in this case). The simplex can be split up into triangles or hexagons and colored according to one of three styles:

  • Triangular -- triangular (default): coloring triangles by summing the values on the vertices
  • Dual-triangular -- dual-triangular: mapping (i,j,k) to the upright triangles △ and blending the neigboring triangles for the downward triangles ▽
  • Hexagonal -- hexagonal: which does not blend values at all, and divides the simplex up into hexagonal regions

The two triangular heatmap styles and the hexagonal heatmap style can be visualized as follows: left is triangular, right is dual triangular.

Thanks to chebee7i for the above images.

Let's define a function on the simplex for illustration, the Shannon entropy of a probability distribution:

    def shannon_entropy(p):
        """Computes the Shannon Entropy at a distribution in the simplex."""
        s = 0.
        for i in range(len(p)):
                s += p[i] * math.log(p[i])
            except ValueError:
        return -1.*s

We can get a heatmap of this function as follows:

    import ternary
    scale = 60

    figure, tax = ternary.figure(scale=scale)
    tax.heatmapf(shannon_entropy, boundary=True, style="triangular")
    tax.set_title("Shannon Entropy Heatmap")

In this case the keyword argument boundary indicates whether you wish to evaluate points on the boundary of the partition (which is sometimes undesirable). Specify style="hexagonal" for hexagons. Large scalings can use a lot of RAM since the number of polygons rendered is O(n^2).

You may specify a matplotlib colormap (an instance or the colormap name) in the cmap argument.

Ternary can also make heatmaps from data. In this case you need to supply a dictionary mapping (i, j) or (i, j, k) for i + j + k = scale to a float as input for a heatmap. It is not necessary to include k in the dictionary keys since it can be determined from scale, i, and j. This reduces the memory requirements when the partition is very fine (significant when scale is in the hundreds).

Make the heatmap as follows:

    ternary.heatmap(data, scale, ax=None, cmap=None)

or on a TernaryAxesSubplot object:

    tax.heatmap(data, cmap=None)

This can produces images such as:

Axes Ticks and Orientations

For a given ternary plot there are two valid ways to label the axes ticks corresponding to the clockwise and counterclockwise orientations. However note that the axes labels need to be adjusted accordingly, and ternary does not do so automatically when you pass clockwise=True to tax.ticks().

There is a more detailed discussion on issue #18 (closed).

RGBA colors

You can alternatively specify colors as rgba tuples (r, g, b, a) (all between zero and one). To use this feature, pass colormap=False to heatmap() so that the library will not attempt to map the tuple to a value with a matplotlib colormap. Note that this disables the inclusion of a colorbar. Here is an example:

import math
from matplotlib import pyplot as plt
import ternary

def color_point(x, y, z, scale):
    w = 255
    x_color = x * w / float(scale)
    y_color = y * w / float(scale)
    z_color = z * w / float(scale)
    r = math.fabs(w - y_color) / w
    g = math.fabs(w - x_color) / w
    b = math.fabs(w - z_color) / w
    return (r, g, b, 1.)

def generate_heatmap_data(scale=5):
    from ternary.helpers import simplex_iterator
    d = dict()
    for (i, j, k) in simplex_iterator(scale):
        d[(i, j, k)] = color_point(i, j, k, scale)
    return d

scale = 80
data = generate_heatmap_data(scale)
figure, tax = ternary.figure(scale=scale)
tax.heatmap(data, style="hexagonal", use_rgba=True)
tax.set_title("RGBA Heatmap")

This produces the following image:


You can run the test suite as follows:

python -m unittest discover tests


Contributions are welcome! Please share any nice example plots, contribute features, and add unit tests! Use the pull request and issue systems to contribute.

Selected Contributors

  • Marc Harper marcharper: maintainer
  • Bryan Weinstein btweinstein: Hexagonal heatmaps, colored trajectory plots
  • chebee7i: Docs and figures, triangular heatmapping
  • Cory Simon: Axis Colors, colored heatmap example


At one point there was an issue on macs that causes the axes labels not to render. The workaround is to manually call


before showing or rendering the image.

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