Math-Animation

Description

The Repository that contains source-code for animations and problems from articles on Habr

Example from Probability theory

DistributionDiceRoll.mp4

import numpy as np

from manim import *
from Dice import *


class DistributionDiceRoll(Scene):
    def construct(self):
        np.random.seed(49312188)
        count_dice = 7
        count_roll = 10**5
        distr_roll = []
    
        for i in range(count_dice):
            roll = np.sum(np.random.randint(1, 7, size=(i + 1, count_roll)), axis=0)
            val = np.zeros((i + 1) * 6)
            for r in roll:
                val[r - 1] += 1
    
            distr_roll.append(val / count_roll)
    
        dice = VGroup(
            *[
                create_dice(np.random.randint(1, 7), 0.75, 0.2)
                for _ in range(count_dice)
            ]
        ).arrange(RIGHT, buff=0.2)
        hist = BarChart(
            distr_roll[0],
            bar_names=[f"{i}" for i in range(1, 7)],
            bar_colors=["#2F58CD" for _ in range(6)],
        ).scale(0.85)
        VGroup(hist, dice).arrange(DOWN, buff=1)
    
        self.play(GrowFromPoint(dice[0], [dice[0].get_bottom()[0], -5, 0]))
        self.play(DrawBorderThenFill(hist[0:2]))
    
        for k in range(1, count_dice):
            new_hist = (
                BarChart(
                    distr_roll[k],
                    bar_names=[f"{i}" for i in range(1, k * 6 + 7)],
                    bar_colors=["#2F58CD" for _ in range(k * 6)],
                )
                .move_to(hist.get_center())
                .scale(0.85)
            )
    
            self.play(
                GrowFromPoint(dice[k], [dice[k].get_bottom()[0], -5, 0]), run_time=0.5
            )
            self.play(ReplacementTransform(hist[0:2], new_hist[0:2]), run_time=0.5)
            hist = new_hist
    
        mean = 3.5 * count_dice
        std = (count_dice * 35 / 12) ** 0.5
        func = lambda t: np.exp(-0.5 * ((t - mean) / std) ** 2) / (
            std * (2 * np.pi) ** 0.5
        )
        func = hist.plot(func, x_range=[0, 6 * (count_dice)], color="#FDE910")
        self.play(Create(func), run_time=1.5, rate_func=rate_functions.ease_in_out_sine)
        self.wait(0.5)