Code for manimation of all Dyck paths with 14 steps

dyck_path_iterator_7.py

from __future__ import annotations

from manim import *

from combpyter import DyckPaths, DyckPath



def draw_path(path: DyckPath, plane: NumberPlane | None = None) -> VGroup:
    if plane is None:
        plane = NumberPlane(x_range=[0, len(path), 1], y_range=[0, path.height(), 1])
    
    height_profile = path.height_profile()
    mobs = []
    for ind in range(len(height_profile) - 1):
        mobs.extend([
            Dot(plane.c2p(ind, height_profile[ind])),
            Line(
                plane.c2p(ind, height_profile[ind]),
                plane.c2p(ind + 1, height_profile[ind + 1]),
                buff=0,
            )
        ])
    mobs.append(Dot(plane.c2p(len(path), 0)))
    path_mobject = VGroup(*mobs)
    
    return VGroup(plane, path_mobject)

class DyckPathIterator(Scene):
    def construct(self):
        self.camera.background_color = "#455D3E"

        title = VGroup(
            Text("Combinatorial Generation:", color=WHITE, font="Gill Sans"),
            Text("Dyck paths", color=WHITE, font="Gill Sans")
        ).arrange(DOWN).scale_to_fit_width(config.frame_width - 1)

        subtitle = Tex(r"$C_7 = \frac{1}{7+1} \binom{2\cdot 7}{7} = 429$ Dyck paths with 14 steps", color=WHITE).scale_to_fit_width(config.frame_width - 2)

        VGroup(title, subtitle).arrange(DOWN, buff=2)

        self.play(Write(title))
        self.wait(1)
        self.play(Write(subtitle))
        self.wait(1)
        

        N = 7
        paths = list(DyckPaths(N))

        plane = NumberPlane(x_range=[0, 2*N, 1], y_range=[0, N, 1])
        plane.scale_to_fit_width(config.frame_width - 1)

        all_path_mobjects = []
        for path in paths:
            plane, path_mobject = draw_path(path, plane)
            for subm in path_mobject.submobjects:
                if isinstance(subm, Dot):
                    path_mobject.remove(subm)
            all_path_mobjects.append(path_mobject)
        
        all_path_mobjects = VGroup(*all_path_mobjects).arrange_in_grid(24, 20, buff=4).set_style(stroke_width=2, stroke_opacity=0.05)
        all_path_mobjects.scale(min((config.frame_width - 1) / all_path_mobjects.width, (config.frame_height - 1) / all_path_mobjects.height))

        self.play(FadeIn(all_path_mobjects), FadeOut(title, subtitle, shift=DOWN))

        plane, path_mobject = draw_path(paths[0], plane)
        self.play(Create(path_mobject), all_path_mobjects[0].animate.set_style(stroke_opacity=0.33))
        for ind, next_path in enumerate(paths[1:]):
            plane, next_path_mobject = draw_path(next_path, plane)
            self.play(
                Transform(path_mobject, next_path_mobject, rate_func=smooth),
                all_path_mobjects[ind+1].animate.set_style(stroke_opacity=0.33),
                run_time=0.2
            )

        self.wait(0.5)
        self.play(FadeOut(path_mobject, shift=DOWN))
        self.wait()
        self.play(FadeOut(all_path_mobjects))
        self.wait(0.15)