3Blue1Brown Videos Source Code

To run a specific scene from a Python file, use the manimgl command.

If you are running a file from a subdirectory and do not want to modify your system path, you may need to append the parent directories to sys.path at the top of your Python file:

import sys
sys.path.append(".")
sys.path.append("..")
sys.path.append("../../")

Then, execute the file using one of the following commands:

• To run the default scene in the file: manimgl <file_name>.py
• To run a specific scene class within the file: manimgl <file_name>.py <SceneName>

manimgl e_field.py
# OR
manimgl e_field.py WavesIn3D

To run the video samples in this repository, follow these steps:

1. Install manimgl from source: The latest published version may not be up to date. Install it directly from the 3b1b/manim repository.
2. Install LaTeX: Ensure a LaTeX distribution is installed on your system. For Ubuntu, use:

   sudo apt install texlive
   sudo apt install texlive-latex-extra
   sudo apt install texlive-fonts-extra
   sudo apt install texlive-science

3. Clone this repository:

   git clone git@github.com:3b1b/videos.git
   cd videos

You can interact with a scene using an iPython terminal by running manimgl with the -se flag and a line number:

manimgl (file name) (scene name) -se (line_number)

Once in interactive mode, use the checkpoint_paste() function to execute code from your clipboard:

• checkpoint_paste(): Runs the code in the clipboard. If the code starts with a comment, the system saves the scene state at that comment. Subsequent calls to code starting with the same comment will revert to that saved state before running.
• checkpoint_paste(skip): Runs the copied code without animations (all run times set to 0).
• checkpoint_paste(record): Runs the animations in the copied code and renders them to a file.

Use get_sum_plot to create a plot of the sum of $n$ variables without standardization. This is useful for showing how the sum distribution shifts and spreads as $n$ increases.

Parameters:

• dist: The base distribution.
• n: Number of variables.
• top_plot: A reference plot (used to match width/scaling).
• x_range: Tuple (min, max) for the x-axis.
• y_range: Tuple (min, max, step) for the y-axis.
• x_num_range: Tuple (start, stop, step) for x-axis tick marks.
• max_width: Maximum width of the plot.

sum_plot = self.get_sum_plot(
    dist, 
    N, 
    top_plot, 
    x_range=(0, 500, 10),
    y_range=(0, 0.05, 0.1),
    x_num_range=(0, 600, 100),
    max_width=14
)

The get_sum(n) method (used within ShowReciprocalSums and its subclasses) generates a LaTeX expression representing the sum of reciprocal odd numbers $\sum_{k=1}^{n} \frac{1}{2k+1}$. It handles truncation using \dots if the number of terms exceeds max_shown_parts.

def get_sum(self, n):
    tex_parts = []
    tally = 0
    msp = self.max_shown_parts
    for k in range(1, n + 1):
        new_parts = [f"1 / {2 * k + 1}", "+"]
        if n > msp:
            if k < msp - 1 or k == n:
                tex_parts.extend(new_parts)
            elif k == msp - 1:
                tex_parts.extend([R"\cdots", "+"])
        else:
            tex_parts.extend(new_parts)
        tally += 1 / (2 * k + 1)
    tex_parts[-1] = "="
    tex_parts.append(R"{:.06f}\dots".format(tally))
    return OldTex(*tex_parts)

Use get_mu_sigma_annotations to generate visual indicators (lines, arrows, and labels) for the mean ($\mu$) and standard deviation ($\sigma$) on a given plot.

Parameters:

• plot: The plot object containing axes and bars.
• mu_tex: LaTeX string for the mean label (e.g., R"\mu").
• sigma_tex: LaTeX string for the standard deviation label (e.g., R"\sigma").
• min_height: Minimum height for the mean line.
• x_min: The minimum x-value for coordinate calculations.

mean_label, sd_label = self.get_mu_sigma_annotations(
    sum_plot, 
    "350", 
    "17.1", 
    min_height=1.0, 
    x_min=n
)

Use get_variable_display(name, color, value_range) to create an interactive UI component consisting of a LaTeX equation, a vertical number line, and a slider. It returns a tuple containing the VGroup (the UI component) and a ValueTracker used to control the value.

• name: The LaTeX string for the variable (e.g., R"\mu").
• color: The color to apply to the variable in the equation and the slider.
• value_range: A tuple (min, max) defining the slider's limits.

Use get_axes(x_range, y_range) to generate a NumberPlane configured for statistical visualizations. The axes are automatically shifted to the bottom of the frame and include formatted numbers on both axes.

• x_range: A tuple (min, max) for the x-axis.
• y_range: A tuple (min, max, step) for the y-axis.

Returns a NumberPlane object.

axes = self.get_axes(
    x_range=(-4, 4),
    y_range=(-1.0, 2.0, 1.0),
)

This module provides mathematical helper functions used for generating graphs and animations related to the Borwein video.

• sinc(x): Computes the normalized sinc function $\frac{\sin(x)}{x}$ using np.sinc(x / PI).
• multi_sinc(x, n): Computes the product of sinc functions $\prod_{k=0}^{n-1} \text{sinc}(\frac{x}{2k+1})$.
• rect_func(x): Returns a rectangular function that is $1.0$ for $-0.5 < x < 0.5$ and $0.0$ otherwise.

def sinc(x):
    return np.sinc(x / PI)

def multi_sinc(x, n):
    return np.prod([sinc(x / (2 * k + 1)) for k in range(n)})

def rect_func(x):
    result = np.zeros_like(x)
    result[(-0.5 < x) & (x < 0.5)] = 1.0
    return result