Create Packed Bubble Charts with Python

Introduction

In this lab, we will learn how to create a packed-bubble chart using Matplotlib in Python. The packed-bubble chart is a type of chart that displays data in bubbles of different sizes, with the bubble's size representing the data's magnitude. This chart is useful for displaying scalar data, where the data is a single numeric value associated with an item.

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Import Required Libraries

To create a packed-bubble chart, we need to import the matplotlib.pyplot and numpy libraries. The numpy library is used to perform mathematical operations on arrays, which is useful for calculating bubble sizes.

import matplotlib.pyplot as plt
import numpy as np

Define Data

The data we will use for this example is the market share of different desktop browsers. We will define the data as a dictionary containing the browser names, market share, and color for each bubble.

browser_market_share = {
    'browsers': ['firefox', 'chrome', 'safari', 'edge', 'ie', 'opera'],
    'market_share': [8.61, 69.55, 8.36, 4.12, 2.76, 2.43],
    'color': ['#5A69AF', '#579E65', '#F9C784', '#FC944A', '#F24C00', '#00B825']
}

Define BubbleChart Class

The BubbleChart class is used to create the packed-bubble chart. The class takes in an array of bubble areas and a bubble spacing value. The __init__ method sets up the initial positions of the bubbles and calculates the maximum step distance, which is the distance each bubble can move in a single iteration.

class BubbleChart:
    def __init__(self, area, bubble_spacing=0):
        """
        Setup for bubble collapse.

        Parameters
        ----------
        area : array-like
            Area of the bubbles.
        bubble_spacing : float, default: 0
            Minimal spacing between bubbles after collapsing.

        Notes
        -----
        If "area" is sorted, the results might look weird.
        """
        area = np.asarray(area)
        r = np.sqrt(area / np.pi)

        self.bubble_spacing = bubble_spacing
        self.bubbles = np.ones((len(area), 4))
        self.bubbles[:, 2] = r
        self.bubbles[:, 3] = area
        self.maxstep = 2 * self.bubbles[:, 2].max() + self.bubble_spacing
        self.step_dist = self.maxstep / 2

        ## calculate initial grid layout for bubbles
        length = np.ceil(np.sqrt(len(self.bubbles)))
        grid = np.arange(length) * self.maxstep
        gx, gy = np.meshgrid(grid, grid)
        self.bubbles[:, 0] = gx.flatten()[:len(self.bubbles)]
        self.bubbles[:, 1] = gy.flatten()[:len(self.bubbles)]

        self.com = self.center_of_mass()

Define Bubble Movement Methods

The BubbleChart class also contains methods to move the bubbles towards the center of mass and check for collisions with other bubbles. The center_of_mass method calculates the center of mass of all the bubbles, and the center_distance method calculates the distance between a bubble and the center of mass. The outline_distance method calculates the distance between a bubble's outline and the outlines of other bubbles, and the check_collisions method checks if a new bubble position collides with other bubbles.

    def center_of_mass(self):
        return np.average(
            self.bubbles[:, :2], axis=0, weights=self.bubbles[:, 3]
        )

    def center_distance(self, bubble, bubbles):
        return np.hypot(bubble[0] - bubbles[:, 0],
                        bubble[1] - bubbles[:, 1])

    def outline_distance(self, bubble, bubbles):
        center_distance = self.center_distance(bubble, bubbles)
        return center_distance - bubble[2] - \
            bubbles[:, 2] - self.bubble_spacing

    def check_collisions(self, bubble, bubbles):
        distance = self.outline_distance(bubble, bubbles)
        return len(distance[distance < 0])

Define Bubble Collision Method

The BubbleChart class also contains a method to check for bubble collisions and move around colliding bubbles. The collides_with method calculates the distance between a new bubble position and the positions of other bubbles. If the distance is less than zero, it means there is a collision, and the method returns the index of the colliding bubble. The collapse method moves the bubbles towards the center of mass and around colliding bubbles, and the plot method draws the bubbles on the chart.

    def collides_with(self, bubble, bubbles):
        distance = self.outline_distance(bubble, bubbles)
        idx_min = np.argmin(distance)
        return idx_min if type(idx_min) == np.ndarray else [idx_min]

    def collapse(self, n_iterations=50):
        """
        Move bubbles to the center of mass.

        Parameters
        ----------
        n_iterations : int, default: 50
            Number of moves to perform.
        """
        for _i in range(n_iterations):
            moves = 0
            for i in range(len(self.bubbles)):
                rest_bub = np.delete(self.bubbles, i, 0)
                ## try to move directly towards the center of mass
                ## direction vector from bubble to the center of mass
                dir_vec = self.com - self.bubbles[i, :2]

                ## shorten direction vector to have length of 1
                dir_vec = dir_vec / np.sqrt(dir_vec.dot(dir_vec))

                ## calculate new bubble position
                new_point = self.bubbles[i, :2] + dir_vec * self.step_dist
                new_bubble = np.append(new_point, self.bubbles[i, 2:4])

                ## check whether new bubble collides with other bubbles
                if not self.check_collisions(new_bubble, rest_bub):
                    self.bubbles[i, :] = new_bubble
                    self.com = self.center_of_mass()
                    moves += 1
                else:
                    ## try to move around a bubble that you collide with
                    ## find colliding bubble
                    for colliding in self.collides_with(new_bubble, rest_bub):
                        ## calculate direction vector
                        dir_vec = rest_bub[colliding, :2] - self.bubbles[i, :2]
                        dir_vec = dir_vec / np.sqrt(dir_vec.dot(dir_vec))
                        ## calculate orthogonal vector
                        orth = np.array([dir_vec[1], -dir_vec[0]])
                        ## test which direction to go
                        new_point1 = (self.bubbles[i, :2] + orth *
                                      self.step_dist)
                        new_point2 = (self.bubbles[i, :2] - orth *
                                      self.step_dist)
                        dist1 = self.center_distance(
                            self.com, np.array([new_point1]))
                        dist2 = self.center_distance(
                            self.com, np.array([new_point2]))
                        new_point = new_point1 if dist1 < dist2 else new_point2
                        new_bubble = np.append(new_point, self.bubbles[i, 2:4])
                        if not self.check_collisions(new_bubble, rest_bub):
                            self.bubbles[i, :] = new_bubble
                            self.com = self.center_of_mass()

            if moves / len(self.bubbles) < 0.1:
                self.step_dist = self.step_dist / 2

    def plot(self, ax, labels, colors):
        """
        Draw the bubble plot.

        Parameters
        ----------
        ax : matplotlib.axes.Axes
        labels : list
            Labels of the bubbles.
        colors : list
            Colors of the bubbles.
        """
        for i in range(len(self.bubbles)):
            circ = plt.Circle(
                self.bubbles[i, :2], self.bubbles[i, 2], color=colors[i])
            ax.add_patch(circ)
            ax.text(*self.bubbles[i, :2], labels[i],
                    horizontalalignment='center', verticalalignment='center')

Create BubbleChart Object and Plot Chart

To create the packed-bubble chart, we need to create a BubbleChart object and call the collapse method to move the bubbles towards the center of mass. We can then create a matplotlib figure and add an axes object to it. Finally, we call the plot method to draw the bubbles on the chart.

bubble_chart = BubbleChart(area=browser_market_share['market_share'],
                           bubble_spacing=0.1)

bubble_chart.collapse()

fig, ax = plt.subplots(subplot_kw=dict(aspect="equal"))
bubble_chart.plot(
    ax, browser_market_share['browsers'], browser_market_share['color'])
ax.axis("off")
ax.relim()
ax.autoscale_view()
ax.set_title('Browser market share')

plt.show()

Summary

In this lab, we learned how to create a packed-bubble chart using Matplotlib in Python. We defined the data as a dictionary containing the browser names, market share, and color for each bubble. We then created a BubbleChart class to set up the initial positions of the bubbles, calculate the maximum step distance, move the bubbles towards the center of mass, and check for collisions with other bubbles. Finally, we plotted the chart using matplotlib.