### Install mpltern from GitHub

Source: https://mpltern.readthedocs.io/en/latest/_sources/installation.rst.txt

Install the development version of mpltern directly from its GitHub repository.

```console
python -m pip install -U git+https://github.com/yuzie007/mpltern.git
```

--------------------------------

### Install mpltern from Conda

Source: https://mpltern.readthedocs.io/en/latest/installation.html

Install the latest released version of mpltern from conda-forge. Ensure conda-forge is added as a channel.

```bash
conda config --add channels conda-forge
conda install mpltern

```

--------------------------------

### Install mpltern Development Version from GitHub

Source: https://mpltern.readthedocs.io/en/latest/installation.html

Install the development version of mpltern directly from its GitHub repository using pip.

```bash
python -m pip install -U git+https://github.com/yuzie007/mpltern.git

```

--------------------------------

### Install mpltern from PyPI

Source: https://mpltern.readthedocs.io/en/latest/_sources/installation.rst.txt

Use this command to install the latest released version of mpltern from the Python Package Index.

```console
python -m pip install -U mpltern
```

--------------------------------

### Add conda-forge channel and install mpltern

Source: https://mpltern.readthedocs.io/en/latest/_sources/installation.rst.txt

Configure your conda environment to use the conda-forge channel and then install mpltern.

```console
conda config --add channels conda-forge
conda install mpltern
```

--------------------------------

### mpltern Plotting Region Fitting Examples

Source: https://mpltern.readthedocs.io/en/latest/_downloads/27c1ed65d83ebb5a7a7d0d855966cb47/02.fit.ipynb

This code snippet demonstrates the different 'fit' options ('rectangle', 'triangle', 'none') available in mpltern's `set_ternary_lim` function. It plots a spiral dataset for each fit type, showing how the plotting region is adjusted. Requires matplotlib and mpltern datasets.

```python
import matplotlib.pyplot as plt
from mpltern.datasets import get_spiral


def set_labels(ax):
    """Set ternary-axis labels."""
    ax.set_tlabel('Top')
    ax.set_llabel('Left')
    ax.set_rlabel('Right')
    ax.taxis.set_label_position("tick1")
    ax.laxis.set_label_position("tick1")
    ax.raxis.set_label_position("tick1")


def plot_frame(ax):
    ax.fill(
        [0.0, 0.0, 1.0, 1.0],
        [0.0, 1.0, 1.0, 0.0],
        ec="r",
        fc="none",
        ls=":",
        transform=ax.transAxes,
        clip_on=False,
        zorder=1.0,
    )
    ax.fill(
        [0.5, 0.0, 1.0],
        [1.0, 0.0, 0.0],
        ec="b",
        fc="none",
        ls=":",
        transform=ax.transAxes,
        clip_on=False,
        zorder=1.0,
    )


fig = plt.figure(figsize=(10.8, 4.8))
fig.subplots_adjust(left=0.075, right=0.925, wspace=0.25)

fits = ["rectangle", "triangle", "none"]
for i, fit in enumerate(fits):
    ax = fig.add_subplot(1, 3, i + 1, projection='ternary')
    ax.plot(*get_spiral(), c="k")
    ax.set_ternary_lim(
        0.1, 0.7,  # tmin, tmax
        0.1, 0.7,  # lmin, lmax
        0.1, 0.7,  # rmin, rmax
        fit=fit,
    )
    set_labels(ax)
    ax.set_title(f"fit='{fit}'", pad=42)

    plot_frame(ax)

plt.show()
```

--------------------------------

### Ternary Contour Plots

Source: https://mpltern.readthedocs.io/en/latest/_downloads/96ad35c4f29e37a0c5b937c9af02b25f/02.contour.ipynb

Generates both `tricontour` and `tricontourf` plots on a ternary diagram. This example requires importing numpy, matplotlib.pyplot, and get_shanon_entropies from mpltern.datasets. It also demonstrates setting color bar scales and labels.

```python
import numpy as np

import matplotlib.pyplot as plt
from mpltern.datasets import get_shanon_entropies

t, l, r, v = get_shanon_entropies()

fig = plt.figure(figsize=(10.8, 4.8))
fig.subplots_adjust(left=0.075, right=0.85, wspace=0.3)

# These values are for controlling the color-bar scale, and here they are
# explicitly given just to make the same color-bar scale for all the plots.
# In general, you may not need to explicitly specify them.
vmin = 0.0
vmax = 1.2
levels = np.linspace(vmin, vmax, 7)

ax = fig.add_subplot(1, 2, 1, projection='ternary')
cs = ax.tricontour(t, l, r, v, levels=levels)
ax.clabel(cs)
ax.set_title("tricontour")

cax = ax.inset_axes([1.05, 0.1, 0.05, 0.9], transform=ax.transAxes)
colorbar = fig.colorbar(cs, cax=cax)
colorbar.set_label('Entropy', rotation=270, va='baseline')

ax = fig.add_subplot(1, 2, 2, projection='ternary')
cs = ax.tricontourf(t, l, r, v, levels=levels)
ax.set_title("tricontourf")

cax = ax.inset_axes([1.05, 0.1, 0.05, 0.9], transform=ax.transAxes)
colorbar = fig.colorbar(cs, cax=cax)
colorbar.set_label('Entropy', rotation=270, va='baseline')

plt.show()
```

--------------------------------

### Ternary Plotting Region Fitting Example

Source: https://mpltern.readthedocs.io/en/latest/gallery/limits/02.fit.html

This snippet demonstrates how to use the 'fit' option in `set_ternary_lim` to control the plotting region. It shows three different fitting modes: 'rectangle' (default), 'triangle', and 'none'. The `plot_frame` function is used to visualize the boundaries.

```python
import matplotlib.pyplot as plt
from mpltern.datasets import get_spiral


def set_labels(ax):
    """Set ternary-axis labels."""
    ax.set_tlabel('Top')
    ax.set_llabel('Left')
    ax.set_rlabel('Right')
    ax.taxis.set_label_position("tick1")
    ax.laxis.set_label_position("tick1")
    ax.raxis.set_label_position("tick1")


def plot_frame(ax):
    ax.fill(
        [0.0, 0.0, 1.0, 1.0],
        [0.0, 1.0, 1.0, 0.0],
        ec="r",
        fc="none",
        ls=":",
        transform=ax.transAxes,
        clip_on=False,
        zorder=1.0,
    )
    ax.fill(
        [0.5, 0.0, 1.0],
        [1.0, 0.0, 0.0],
        ec="b",
        fc="none",
        ls=":",
        transform=ax.transAxes,
        clip_on=False,
        zorder=1.0,
    )


fig = plt.figure(figsize=(10.8, 4.8))
fig.subplots_adjust(left=0.075, right=0.925, wspace=0.25)

fits = ["rectangle", "triangle", "none"]
for i, fit in enumerate(fits):
    ax = fig.add_subplot(1, 3, i + 1, projection='ternary')
    ax.plot(*get_spiral(), c="k")
    ax.set_ternary_lim(
        0.1, 0.7,  # tmin, tmax
        0.1, 0.7,  # lmin, lmax
        0.1, 0.7,  # rmin, rmax
        fit=fit,
    )
    set_labels(ax)
    ax.set_title(f"fit='{fit}'", pad=42)

    plot_frame(ax)

plt.show()

```

--------------------------------

### Plotting Lines and Curves on Ternary Plot

Source: https://mpltern.readthedocs.io/en/latest/_downloads/5e6f20e02c879cc16d98d723b1ecdea9/00.line_and_curve.ipynb

Plots multiple lines and curves on a ternary diagram. Includes examples of straight lines, lines with markers, dashed lines with markers, and a custom spiral curve. Requires importing matplotlib.pyplot and mpltern.datasets.

```python
import matplotlib.pyplot as plt
from mpltern.datasets import get_spiral


ax = plt.subplot(projection='ternary')

ax.plot([0.8, 0.6], [0.1, 0.2], [0.1, 0.2])
ax.plot([0.1, 0.2], [0.8, 0.6], [0.1, 0.2], marker='o')
ax.plot([0.1, 0.2], [0.1, 0.2], [0.8, 0.6], ls=':', marker='s', mfc='none')

t, l, r = get_spiral()
ax.plot(t, l, r, color='k')

plt.show()
```

--------------------------------

### Import mpltern and Matplotlib

Source: https://mpltern.readthedocs.io/en/latest/_sources/basic_usage.rst.txt

Import the necessary libraries to begin using mpltern. This registers the 'ternary' projection.

```python
import matplotlib.pyplot as plt
import mpltern
```

--------------------------------

### Setting Ternary Plot Aspect Ratio

Source: https://mpltern.readthedocs.io/en/latest/_downloads/081109d37f398f53db66f3bbd9e53685/00.aspect.ipynb

Use `ax.set_aspect` to control the aspect ratio of a ternary plot. This example shows setting it to 1.5.

```python
import matplotlib.pyplot as plt
from mpltern.datasets import get_spiral


ax = plt.subplot(projection='ternary')
ax.plot(*get_spiral())

ax.set_aspect(1.5)

ax.set_tlabel('Top')
ax.set_llabel('Left')
ax.set_rlabel('Right')

plt.show()
```

--------------------------------

### Import Libraries and Data

Source: https://mpltern.readthedocs.io/en/latest/_downloads/a9754b9e965bd1513dff9cab1e73b865/01.style_sheets.ipynb

Imports necessary libraries (matplotlib.pyplot) and a sample dataset (get_spiral) for plotting.

```python
import matplotlib.pyplot as plt
from mpltern.datasets import get_spiral
```

--------------------------------

### Control Tick Label Rotation

Source: https://mpltern.readthedocs.io/en/latest/gallery/axis_and_tick/12.tick_rotation.html

Modify tick rotation using `ax.tick_params(labelrotation=...)`. This example shows different rotation options: 'tick', 'axis', and 'horizontal'.

```python
import matplotlib.pyplot as plt
import mpltern

fig = plt.figure(figsize=(10.8, 4.8))
fig.subplots_adjust(left=0.075, right=0.925, wspace=0.25)

for i, labelrotation in enumerate(["tick", "axis", "horizontal"]):
    ax = fig.add_subplot(1, 3, i + 1, projection='ternary')
    ax.tick_params(labelrotation=labelrotation)
    ax.set_title(f"labelrotation='{labelrotation}'", pad=36)

plt.show()

```

--------------------------------

### Import Libraries and Generate Data

Source: https://mpltern.readthedocs.io/en/latest/_downloads/755f011432021d4601fa0c293adfba27/hexbin.ipynb

Imports necessary libraries (numpy, matplotlib, mpltern) and generates sample ternary data using `np.random.dirichlet`. This data is used for creating hexbin plots.

```python
import numpy as np

import matplotlib.pyplot as plt
import mpltern

np.random.seed(19680801)
t, l, r = np.random.dirichlet(alpha=(2.0, 4.0, 8.0), size=100000).T
```

--------------------------------

### Plotting on an Arbitrary Triangle

Source: https://mpltern.readthedocs.io/en/latest/_downloads/5853751a4cba801ea4f1ce1401ed31f4/02.arbitrary_triangle.ipynb

Use this snippet to create a ternary plot with custom corner coordinates. Ensure matplotlib and mpltern are installed. The `get_spiral` function is used here for demonstration purposes.

```python
import matplotlib.pyplot as plt
from mpltern.datasets import get_spiral

corners = ((0.0, 0.0), (0.5, 0.5), (-0.5, 1.0))
ax = plt.subplot(projection='ternary', corners=corners)

ax.plot(*get_spiral())

ax.set_tlabel('Top')
ax.set_llabel('Left')
ax.set_rlabel('Right')

ax.grid()

plt.show()
```

--------------------------------

### Adding a Legend to a Ternary Plot

Source: https://mpltern.readthedocs.io/en/latest/_downloads/6ca0d2e0b0fd73bb5246b635495e0b86/legend.ipynb

This snippet shows how to create a ternary plot and add a legend to it. It uses `numpy` for data generation and `matplotlib.pyplot` with `mpltern` for plotting. Ensure `mpltern` is installed.

```python
import numpy as np

import matplotlib.pyplot as plt
import mpltern


ax = plt.subplot(projection="ternary")

np.random.seed(19680801)
for i in range(4):
    t, l, r = np.random.dirichlet(alpha=(2.0, 2.0, 2.0), size=10).T
    ax.scatter(t, l, r, alpha=0.5, label=i)

ax.legend()

plt.show()
```

--------------------------------

### Import mpltern and Matplotlib

Source: https://mpltern.readthedocs.io/en/latest/basic_usage.html

Import the necessary libraries, mpltern and Matplotlib, to begin creating ternary plots.

```python
import matplotlib.pyplot as plt
import mpltern

```

--------------------------------

### Set Ternary Axis Label Rotation Mode

Source: https://mpltern.readthedocs.io/en/latest/_downloads/f36124de34d49d39108f712ea6bf98eb/01.axis_label_rotation.ipynb

Apply different label rotation modes ('axis' or 'horizontal') to ternary plot axes. This example visualizes the effect of each mode on the axis labels.

```python
import matplotlib.pyplot as plt
from mpltern.datasets import get_spiral


pad = 42

t, l, r = get_spiral()

fig = plt.figure(figsize=(10.8, 4.8))
fig.subplots_adjust(wspace=0.3)

modes = ['axis', 'horizontal']
for i, mode in enumerate(modes):
    ax = fig.add_subplot(1, 2, i + 1, projection='ternary')

    ax.plot(t, l, r)

    ax.set_tlabel('Top')
    ax.set_llabel('Left')
    ax.set_rlabel('Right')

    ax.taxis.set_label_rotation_mode(mode)
    ax.laxis.set_label_rotation_mode(mode)
    ax.raxis.set_label_rotation_mode(mode)

    ax.set_title("label_rotation_mode='{}'".format(mode), pad=pad)

plt.show()
```

--------------------------------

### Replicator Equation Visualization

Source: https://mpltern.readthedocs.io/en/latest/_downloads/abfa4b9c1e00efb75b6afa1fc1511bd6/evolutionary_game_theory.ipynb

Visualizes the dynamics of the replicator equation using a payoff matrix and ternary plots. Requires matplotlib, numpy, and mpltern. The code calculates fitness, determines the direction of change (d), and plots the results on a ternary diagram with quiver arrows indicating strategy evolution.

```python
import matplotlib.pyplot as plt
import numpy as np
from mpltern.datasets import get_triangular_grid

x = np.array(get_triangular_grid(25))

payoff_matrix = [
    [0.0, -1.0, 1.0],
    [1.0, 0.0, -1.0],
    [-1.0, 1.0, 0.0],
]

fitness = payoff_matrix @ x
d = (fitness - np.sum(fitness * x, axis=0)) * x
norm = np.linalg.norm(d, axis=0)

ax = plt.subplot(projection="ternary")

ax.tripcolor(*x, norm, cmap="turbo", shading="gouraud", rasterized=True)

ax.quiver(*x, *d, scale=5, clip_on=False)

ax.set_tlabel("$x_0$")
ax.set_llabel("$x_1$")
ax.set_rlabel("$x_2$")

plt.show()
```

--------------------------------

### Import Libraries

Source: https://mpltern.readthedocs.io/en/latest/gallery/intermediate/01.style_sheets.html

Imports necessary libraries for plotting and data retrieval.

```python
import matplotlib.pyplot as plt
from mpltern.datasets import get_spiral

```

--------------------------------

### Create TernaryAxes with Custom Sum and Labels

Source: https://mpltern.readthedocs.io/en/latest/_sources/basic_usage.rst.txt

Create a TernaryAxes with a specified normalization constant (ternary_sum) and set custom labels for the top, left, and right axes. Also adds a grid.

```python
ax = plt.subplot(projection="ternary", ternary_sum=100.0)

ax.set_tlabel("Top (%)")
ax.set_llabel("Left (%)")
ax.set_rlabel("Right (%)")

ax.grid()

plt.show()
```

--------------------------------

### Set Manual Tick Positions in Ternary Plot

Source: https://mpltern.readthedocs.io/en/latest/_downloads/0e540e7d76806b323fbb3aec4f2380e6/30.manual_tick_positions.ipynb

Use `set_ticks()` on the respective axis objects (taxis, laxis, raxis) to manually define tick positions. This example plots a spiral and customizes the ticks on all three axes.

```python
import matplotlib.pyplot as plt
from mpltern.datasets import get_spiral


ax = plt.subplot(projection='ternary')

ax.plot(*get_spiral())

ax.grid()

ax.set_tlabel('Top')
ax.set_llabel('Left')
ax.set_rlabel('Right')

# Specify tick positions manually.
ax.taxis.set_ticks([0.2, 0.4, 0.6, 0.8, 1.0])
ax.laxis.set_ticks([0.2, 0.4, 0.6, 0.8, 1.0])
ax.raxis.set_ticks([0.2, 0.4, 0.6, 0.8, 1.0])

plt.show()
```

--------------------------------

### Plotting Arrows on Ternary Diagram

Source: https://mpltern.readthedocs.io/en/latest/_downloads/0980e039de204273861bea5734d43435/08.quiver.ipynb

Plots a 2D field of arrows on a ternary diagram. The sum of the three components (dt, dl, dr) must be zero. This example shows plotting with default arrow length and with a specified length.

```python
import numpy as np

import matplotlib.pyplot as plt
from mpltern.datasets import get_triangular_grid


t, l, r = get_triangular_grid()

# Arrows. The sum of the three must be zero.
dt = 1.0 / 3.0 - t
dl = 1.0 / 3.0 - l
dr = 1.0 / 3.0 - r

length = np.sqrt(dt ** 2 + dl ** 2 + dr ** 2)

fig = plt.figure(figsize=(10.8, 4.8))
fig.subplots_adjust(left=0.075, right=0.85, wspace=0.3)

ax = fig.add_subplot(121, projection='ternary')
pc = ax.quiver(t, l, r, dt, dl, dr)

ax = fig.add_subplot(122, projection='ternary')
pc = ax.quiver(t, l, r, dt, dl, dr, length)

cax = ax.inset_axes([1.05, 0.1, 0.05, 0.9], transform=ax.transAxes)
colorbar = fig.colorbar(pc, cax=cax)
colorbar.set_label('Length', rotation=270, va='baseline')

plt.show()
```

--------------------------------

### Mpltern Logo Generation Functions

Source: https://mpltern.readthedocs.io/en/latest/_sources/gallery/miscellaneous/00.logos.rst.txt

Defines helper functions to create the mpltern logo, including functions for creating axes with ternary spans and axes for text rendering. It also includes the main function to generate the full figure.

```Python
import matplotlib.pyplot as plt

import matplotlib.font_manager
from matplotlib.patches import PathPatch
from matplotlib.text import TextPath
import matplotlib.transforms as mtrans
import mpltern  # noqa: F401

MPL_BLUE = '#11557c'


def get_font_properties():
    return matplotlib.font_manager.FontProperties(weight='bold')


def create_icon_axes(fig, ax_position, lw_grid, lw_border):
    """
    Create a ternary axes containing the mpltern span plot.

    Parameters
    ----------
    fig : matplotlib.figure.Figure
        The figure to draw into.
    ax_position : (float, float, float, float)
        The position of the created Axes in figure coordinates as
        (x, y, width, height).
    lw_grid : float
        The linewidth of the grid.
    lw_border : float
        The linewidth of the Axes border.

    Returns
    -------
    ax : matplotlib.axes.Axes
        The created Axes.
    """
    with plt.rc_context({'axes.edgecolor': MPL_BLUE,
                         'axes.linewidth': lw_border}):
        ax = fig.add_axes(ax_position, projection='ternary')

        ax.axtspan(0.4, 0.6, color='C0', alpha=0.6)
        ax.axlspan(0.4, 0.6, color='C1', alpha=0.6)
        ax.axrspan(0.4, 0.6, color='C2', alpha=0.6)

        ax.tick_params(
            tick1On=False, tick2On=False, label1On=False, label2On=False)

        ax.grid(lw=lw_grid, color='0.9')
        # the actual visible background - extends a bit beyond the axis
        ax.fill(
            (1.04, -0.02, -0.02),
            (-0.02, 1.04, -0.02),
            (-0.02, -0.02, 1.04),
            facecolor='white', zorder=0,
            clip_on=False, in_layout=False)
        return ax


def create_text_axes(fig, height_px):
    """Create an Axes in *fig* that contains 'mpltern' as Text."""
    ax = fig.add_axes((0, 0, 1, 1))
    ax.set_aspect("equal")
    ax.set_axis_off()

    path = TextPath((0, 0), "mpl  tern", size=height_px * 0.8,
                    prop=get_font_properties())

    angle = 4.25  # degrees
    trans = mtrans.Affine2D().skew_deg(angle, 0)

    patch = PathPatch(path, transform=trans + ax.transData, color=MPL_BLUE,
                      lw=0)
    ax.add_patch(patch)
    ax.autoscale()


def make_logo(height_px, lw_grid, lw_border, with_text=False):
    """
    Create a full figure with the mpltern logo.

    Parameters
    ----------
    height_px : int
        Height of the figure in pixel.
    lw_grid : float
        The linewidth of the grid.
    lw_border : float
        The linewidth of icon border.
    with_text : bool
        Whether to draw only the icon or to include 'mpltern' as text.
    """
    dpi = 100
    height = height_px / dpi
    figsize = (5 * height, height) if with_text else (height, height)
    fig = plt.figure(figsize=figsize, dpi=dpi)
    fig.patch.set_alpha(0)

    if with_text:
        create_text_axes(fig, height_px)

    ax_pos = (0.395, 0.12, .17, 0.75) if with_text else (0.1, 0.1, 0.8, 0.8)
    ax = create_icon_axes(fig, ax_pos, lw_grid, lw_border)

    return fig, ax

```

--------------------------------

### Generate Mpltern Logo with Text

Source: https://mpltern.readthedocs.io/en/latest/_downloads/fa8c7f59a477102d318377608aa3d48c/00.logos.ipynb

Generates a large Mpltern logo that includes the 'mpltern' text. This version is used on the Mpltern website. Ensure `plt.show()` is called to display the figure.

```python
make_logo(height_px=110, lw_grid=0.5, lw_border=1,
          with_text=True)
plt.show()
```

--------------------------------

### Create Ternary Axes with Custom Sum and Labels

Source: https://mpltern.readthedocs.io/en/latest/basic_usage.html

Create a ternary axes with a custom normalization constant (ternary_sum) and set custom labels for the top, left, and right axes. A grid is also added.

```python
ax = plt.subplot(projection="ternary", ternary_sum=100.0)

ax.set_tlabel("Top (%)")
ax.set_llabel("Left (%)")
ax.set_rlabel("Right (%)")

ax.grid()

plt.show()

```

--------------------------------

### Generate Mpltern Logo Icon

Source: https://mpltern.readthedocs.io/en/latest/_downloads/fa8c7f59a477102d318377608aa3d48c/00.logos.ipynb

This function creates a ternary axes with Mpltern's logo icon. It sets up the axes, adds spans, ticks, grid, and a background fill. Use this for generating the core icon.

```python
import matplotlib.pyplot as plt

import matplotlib.font_manager
from matplotlib.patches import PathPatch
from matplotlib.text import TextPath
import matplotlib.transforms as mtrans
import mpltern  # noqa: F401

MPL_BLUE = '#11557c'


def get_font_properties():
    return matplotlib.font_manager.FontProperties(weight='bold')


def create_icon_axes(fig, ax_position, lw_grid, lw_border):
    """
    Create a ternary axes containing the mpltern span plot.

    Parameters
    ----------
    fig : matplotlib.figure.Figure
        The figure to draw into.
    ax_position : (float, float, float, float)
        The position of the created Axes in figure coordinates as
        (x, y, width, height).
    lw_grid : float
        The linewidth of the grid.
    lw_border : float
        The linewidth of the Axes border.

    Returns
    -------
    ax : matplotlib.axes.Axes
        The created Axes.
    """
    with plt.rc_context({'axes.edgecolor': MPL_BLUE,
                         'axes.linewidth': lw_border}):
        ax = fig.add_axes(ax_position, projection='ternary')

        ax.axtspan(0.4, 0.6, color='C0', alpha=0.6)
        ax.axlspan(0.4, 0.6, color='C1', alpha=0.6)
        ax.axrspan(0.4, 0.6, color='C2', alpha=0.6)

        ax.tick_params(
            tick1On=False, tick2On=False, label1On=False, label2On=False)

        ax.grid(lw=lw_grid, color='0.9')
        # the actual visible background - extends a bit beyond the axis
        ax.fill(
            (1.04, -0.02, -0.02),
            (-0.02, 1.04, -0.02),
            (-0.02, -0.02, 1.04),
            facecolor='white', zorder=0,
            clip_on=False, in_layout=False)
        return ax


def create_text_axes(fig, height_px):
    """Create an Axes in *fig* that contains 'mpltern' as Text."""
    ax = fig.add_axes((0, 0, 1, 1))
    ax.set_aspect("equal")
    ax.set_axis_off()

    path = TextPath((0, 0), "mpl  tern", size=height_px * 0.8,
                    prop=get_font_properties())

    angle = 4.25  # degrees
    trans = mtrans.Affine2D().skew_deg(angle, 0)

    patch = PathPatch(path, transform=trans + ax.transData, color=MPL_BLUE,
                      lw=0)
    ax.add_patch(patch)
    ax.autoscale()


def make_logo(height_px, lw_grid, lw_border, with_text=False):
    """
    Create a full figure with the mpltern logo.

    Parameters
    ----------
    height_px : int
        Height of the figure in pixel.
    lw_grid : float
        The linewidth of the grid.
    lw_border : float
        The linewidth of icon border.
    with_text : bool
        Whether to draw only the icon or to include 'mpltern' as text.
    """
    dpi = 100
    height = height_px / dpi
    figsize = (5 * height, height) if with_text else (height, height)
    fig = plt.figure(figsize=figsize, dpi=dpi)
    fig.patch.set_alpha(0)

    if with_text:
        create_text_axes(fig, height_px)

    ax_pos = (0.395, 0.12, .17, 0.75) if with_text else (0.1, 0.1, 0.8, 0.8)
    ax = create_icon_axes(fig, ax_pos, lw_grid, lw_border)

    return fig, ax
```

--------------------------------

### Generate Small Mpltern Logo

Source: https://mpltern.readthedocs.io/en/latest/_downloads/fa8c7f59a477102d318377608aa3d48c/00.logos.ipynb

Generates a small Mpltern logo icon, suitable for favicons or small UI elements. The line widths are scaled down accordingly.

```python
make_logo(height_px=32, lw_grid=0.3, lw_border=0.3)
```

--------------------------------

### Replicator Equation Visualization

Source: https://mpltern.readthedocs.io/en/latest/gallery/miscellaneous/evolutionary_game_theory.html

Visualizes the replicator equation using a ternary plot. This snippet requires matplotlib and numpy. It calculates fitness based on a payoff matrix and displays the evolution of strategies.

```python
import matplotlib.pyplot as plt
import numpy as np
from mpltern.datasets import get_triangular_grid

x = np.array(get_triangular_grid(25))

payoff_matrix = [
    [0.0, -1.0, 1.0],
    [1.0, 0.0, -1.0],
    [-1.0, 1.0, 0.0],
]

fitness = payoff_matrix @ x
d = (fitness - np.sum(fitness * x, axis=0)) * x
norm = np.linalg.norm(d, axis=0)

ax = plt.subplot(projection="ternary")

ax.tripcolor(*x, norm, cmap="turbo", shading="gouraud", rasterized=True)

ax.quiver(*x, *d, scale=5, clip_on=False)

ax.set_tlabel("$x_0$")
ax.set_llabel("$x_1$")
ax.set_rlabel("$x_2$")

plt.show()

```

--------------------------------

### Plotting with Custom Ternary Sum

Source: https://mpltern.readthedocs.io/en/latest/_downloads/b96d93b7134470913bc470b599eb8a63/04.normalization.ipynb

Demonstrates how to create a ternary plot with a custom normalization sum (e.g., 100.0). The data is automatically normalized according to the specified `ternary_sum`.

```python
import matplotlib.pyplot as plt
from mpltern.datasets import get_spiral


fig = plt.figure()
ax = fig.add_subplot(projection='ternary', ternary_sum=100.0)
t, l, r = get_spiral()
ax.plot(t, l, r)  # Data are automatically normalized by ``ternary_sum``.
plt.show()
```

--------------------------------

### Basic TriBin Plot

Source: https://mpltern.readthedocs.io/en/latest/_downloads/91b975661f3214a0e9e6a98542b01c7b/tribin.ipynb

Creates a basic TriBin plot using default settings. It's recommended to set 'edgecolors="none"' to avoid overlapping visual artifacts with small triangles.

```python
ax = plt.subplot(projection="ternary")

# If "edgecolors=face" (default), small triangles look overlapping.
ax.tribin(t, l, r, edgecolors="none")

plt.show()
```

--------------------------------

### mpltern.ternary.TernaryAxes.hexbin

Source: https://mpltern.readthedocs.io/en/latest/_sources/api.rst.txt

Creates a hexagonal binning plot.

```APIDOC
## mpltern.ternary.TernaryAxes.hexbin

### Description
Creates a hexagonal binning plot.

### Method
(Method details not provided in source)

### Parameters
(Parameter details not provided in source)

### Request Example
(Request example not provided in source)

### Response
(Response details not provided in source)
```

--------------------------------

### mpltern.ternary.TernaryAxes.tribin

Source: https://mpltern.readthedocs.io/en/latest/_sources/api.rst.txt

Creates a triangular binning plot.

```APIDOC
## mpltern.ternary.TernaryAxes.tribin

### Description
Creates a triangular binning plot.

### Method
(Method details not provided in source)

### Parameters
(Parameter details not provided in source)

### Request Example
(Request example not provided in source)

### Response
(Response details not provided in source)
```

--------------------------------

### Plotting Lines and Regions with Ternary Transforms

Source: https://mpltern.readthedocs.io/en/latest/_downloads/244a00f379e58c9228d3cf25c43a1e17/01.ticks.ipynb

Demonstrates plotting lines and filling regions along the t, l, and r axes using their respective transforms. This is useful for visualizing data ranges or specific conditions on a ternary plot.

```python
import matplotlib.pyplot as plt
import mpltern  # noqa: F401

ax = plt.subplot(projection="ternary", ternary_sum=100.0)

x0 = 0.0
x1 = 100.0

ax.plot([x0, x1], [0.5, 0.5], transform=ax.get_taxis_transform())
ax.plot([x0, x1], [0.5, 0.5], transform=ax.get_laxis_transform())
ax.plot([x0, x1], [0.5, 0.5], transform=ax.get_raxis_transform())

y = [0.4, 0.6]

ax.fill_betweenx(y, x0, x1, alpha=0.2, transform=ax.get_taxis_transform())
ax.fill_betweenx(y, x0, x1, alpha=0.2, transform=ax.get_laxis_transform())
ax.fill_betweenx(y, x0, x1, alpha=0.2, transform=ax.get_raxis_transform())

plt.show()
```

--------------------------------

### Plotting a Triangular Grid

Source: https://mpltern.readthedocs.io/en/latest/_downloads/de839b78b8414ca90e384ae5258d2883/11.triangular_grid.ipynb

Generates and plots a triangular grid. Use this to visualize data distributed across three components.

```python
import matplotlib.pyplot as plt
from mpltern.datasets import get_triangular_grid


t, l, r = get_triangular_grid()

fig = plt.figure(figsize=(10.8, 4.8))
fig.subplots_adjust(wspace=0.3)

ax = fig.add_subplot(121, projection='ternary')
ax.triplot(t, l, r)

ax = fig.add_subplot(122, projection='ternary')
ax.triplot(t, l, r, marker='o')

plt.show()
```

--------------------------------

### Basic Hexbin Plot on Ternary Diagram

Source: https://mpltern.readthedocs.io/en/latest/_downloads/755f011432021d4601fa0c293adfba27/hexbin.ipynb

Creates a basic hexbin plot on a ternary diagram using `ax.hexbin`. The `edgecolors='none'` argument is used to prevent overlapping appearance of small hexagons.

```python
ax = plt.subplot(projection="ternary")

# If "edgecolors=face" (default), small hexagons look overlapping.
ax.hexbin(t, l, r, edgecolors="none")

plt.show()
```

--------------------------------

### Hexbin and Scatter Plot on Ternary Diagram

Source: https://mpltern.readthedocs.io/en/latest/_downloads/92412ddc0eefd06ab8f60f2963f0e94d/with_scatter.ipynb

Use this snippet to create a ternary plot showing a hexbin density distribution overlaid with individual scatter points. Requires `numpy`, `matplotlib`, and `mpltern`. Ensure data is generated using `np.random.dirichlet` or similar.

```python
import numpy as np

import matplotlib.pyplot as plt
import mpltern

np.random.seed(19680801)
t, l, r = np.random.dirichlet(alpha=(2.0, 2.0, 2.0), size=100).T

fig = plt.figure(figsize=(10.8, 4.8))
fig.subplots_adjust(left=0.075, right=0.85, wspace=0.3)

ax = fig.add_subplot(1, 2, 1, projection="ternary")
ax.scatter(t, l, r, color="C3", marker="x")
pc = ax.hexbin(t, l, r, gridsize=10, edgecolors="k", alpha=0.5, zorder=0.0)
ax.set_title("hexbin")

cax = ax.inset_axes([1.05, 0.1, 0.05, 0.9], transform=ax.transAxes)
colorbar = fig.colorbar(pc, cax=cax)
colorbar.set_label("Count", rotation=270, va="baseline")

ax = fig.add_subplot(1, 2, 2, projection="ternary")
ax.scatter(t, l, r, color="C3", marker="x")
pc = ax.tribin(t, l, r, gridsize=10, edgecolors="k", alpha=0.5, zorder=0.0)
ax.set_title("tribin")

cax = ax.inset_axes([1.05, 0.1, 0.05, 0.9], transform=ax.transAxes)
colorbar = fig.colorbar(pc, cax=cax)
colorbar.set_label("Count", rotation=270, va="baseline")

plt.show()
```

--------------------------------

### mpltern.ternary.TernaryAxes.axlline

Source: https://mpltern.readthedocs.io/en/latest/_sources/api.rst.txt

Draws a line along the left axis.

```APIDOC
## mpltern.ternary.TernaryAxes.axlline

### Description
Draws a line along the left axis.

### Method
(Method details not provided in source)

### Parameters
(Parameter details not provided in source)

### Request Example
(Request example not provided in source)

### Response
(Response details not provided in source)
```

--------------------------------

### Plot Data on a Ternary Axes

Source: https://mpltern.readthedocs.io/en/latest/basic_usage.html

Demonstrates how to plot data points (t, l, r) on a ternary axes using the ax.plot method, similar to standard Matplotlib plotting.

```python
from mpltern.datasets import get_spiral

ax = plt.subplot(projection="ternary")

t, l, r = get_spiral()
# t: [0.33333333 0.33357906 0.33430414 ...]
# l: [0.33333333 0.33455407 0.33543547 ...]
# r: [0.33333333 0.33186687 0.33026039 ...]
ax.plot(t, l, r)

plt.show()

```

--------------------------------

### Creating an Inset Ternary Plot

Source: https://mpltern.readthedocs.io/en/latest/_downloads/862273d3786ea479e2550d8a5cefcd48/99.inset.ipynb

This snippet demonstrates how to create a main ternary plot and then add an inset ternary plot. It includes setting up random data, plotting scatter points on both axes, and defining the region for the inset. The inset axes are created using `fig.add_axes` with specified figure coordinates and their plotting range is limited using `set_ternary_min`.

```python
import numpy as np

import matplotlib.pyplot as plt
import mpltern


np.random.seed(seed=19)
t0, l0, r0 = np.random.dirichlet(alpha=(2.0, 2.0, 2.0), size=100).T

np.random.seed(seed=68)
t1, l1, r1 = np.random.dirichlet(alpha=(2.0, 2.0, 2.0), size=100).T

fig = plt.figure()
fig.subplots_adjust(left=-0.1)

ax = fig.add_subplot(projection="ternary")

ax.scatter(t0, l0, r0, alpha=0.5)
ax.scatter(t1, l1, r1, alpha=0.5)

# Plot the triangle region for the inset.
ax.fill([0.4, 0.3, 0.3], [0.3, 0.4, 0.3], [0.3, 0.3, 0.4], fc="none", ec="k")

# Create a new `TernaryAxes` for the inset with specifying a rectangle in the
# figure coordinates.
axins = fig.add_axes([0.625, 0.525, 0.30, 0.30], projection="ternary")

# Limit the ploting range to be consistent with the above plotted triangle.
axins.set_ternary_min(0.3, 0.3, 0.3)

axins.scatter(t0, l0, r0, alpha=0.5)
axins.scatter(t1, l1, r1, alpha=0.5)

plt.show()
```

--------------------------------

### TriBin Plot with Logarithmic Binning

Source: https://mpltern.readthedocs.io/en/latest/_downloads/91b975661f3214a0e9e6a98542b01c7b/tribin.ipynb

Generates a TriBin plot with logarithmic binning. This is useful for visualizing data with a wide range of densities.

```python
ax = plt.subplot(projection="ternary")

ax.tribin(t, l, r, bins="log", edgecolors="none")

plt.show()
```

--------------------------------

### Plotting Dirichlet PDFs

Source: https://mpltern.readthedocs.io/en/latest/_sources/gallery/miscellaneous/dirichlet_pdf.rst.txt

Generates and plots the probability density functions for different Dirichlet distributions on ternary diagrams. This is useful for visualizing how the shape of the distribution changes with different alpha parameters.

```Python
import matplotlib.pyplot as plt
from mpltern.datasets import get_dirichlet_pdfs

fig = plt.figure(figsize=(10.8, 8.8))
fig.subplots_adjust(
    left=0.1,
    right=0.9,
    bottom=0.1,
    top=0.9,
    wspace=0.5,
    hspace=0.5,
)

alphas = ((1.5, 1.5, 1.5), (5.0, 5.0, 5.0), (1.0, 2.0, 2.0), (2.0, 4.0, 8.0))
for i, alpha in enumerate(alphas):
    ax = fig.add_subplot(2, 2, i + 1, projection="ternary")
    t, l, r, v = get_dirichlet_pdfs(n=61, alpha=alpha)
    cmap = "Blues"
    shading = "gouraud"
    cs = ax.tripcolor(t, l, r, v, cmap=cmap, shading=shading, rasterized=True)
    ax.tricontour(t, l, r, v, colors="k", linewidths=0.5)

    ax.set_tlabel("$x_1$")
    ax.set_llabel("$x_2$")
    ax.set_rlabel("$x_3$")

    ax.taxis.set_label_position("tick1")
    ax.laxis.set_label_position("tick1")
    ax.raxis.set_label_position("tick1")

    ax.set_title("${\mathbf{\alpha}}$ = " + str(alpha))

    cax = ax.inset_axes([1.05, 0.1, 0.05, 0.9], transform=ax.transAxes)
    colorbar = fig.colorbar(cs, cax=cax)
    colorbar.set_label("PDF", rotation=270, va="baseline")

plt.show()
```

--------------------------------

### Hexbin Plot with Logarithmic Binning

Source: https://mpltern.readthedocs.io/en/latest/_downloads/755f011432021d4601fa0c293adfba27/hexbin.ipynb

Generates a hexbin plot on a ternary diagram with logarithmic binning applied. This is useful for visualizing data with a wide range of counts per bin.

```python
ax = plt.subplot(projection="ternary")

ax.hexbin(t, l, r, bins="log", edgecolors="none")

plt.show()
```