Nice animations

[NickHu]

Thanks @regular-citizen for the Manim export, I was able to pretty easily hack together a nice animation of the 3D associator!

Here's my cleaned-up (ish) code if anyone is interested:

# Uncomment line below if needed
from manim import *
from manim.opengl import *
#import numpy as np

class HomotopyIoManim(Scene):
    def depth(self):
      return 3

    def get_colors(self):
        colors = {
            "generator_1_1": "#c0392b",
            "generator_2_2": "#f39c12",
            "generator_3_3": "#8e44ad",
        }
        return colors

    # Wires
    def get_wires_r0(self):
        C = self.get_colors()
        wires = OpenGLVMobject()
        wires.start_new_path(np.array([2,0,0]))
        wires.add_line_to(np.array([2,1,0]))
        wires.add_cubic_bezier_curve_to(np.array([2,1.8,0]),np.array([2.4,2,0]),np.array([3,2,0]))
        wires.add_line_to(np.array([3,3,0]))
        wires.add_cubic_bezier_curve_to(np.array([3,3.8,0]),np.array([3.6,4,0]),np.array([4.5,4,0]))
        wires.add_line_to(np.array([4.5,6,0]))
        wires.start_new_path(np.array([4,0,0]))
        wires.add_line_to(np.array([4,1,0]))
        wires.add_cubic_bezier_curve_to(np.array([4,1.8,0]),np.array([3.6,2,0]),np.array([3,2,0]))
        wires.start_new_path(np.array([6,0,0]))
        wires.add_line_to(np.array([6,3,0]))
        wires.add_cubic_bezier_curve_to(np.array([6,3.8,0]),np.array([5.4,4,0]),np.array([4.5,4,0]))
        wires.set_stroke(color=C["generator_1_1"],width=5)
        return wires

    def get_wires_s0(self):
        C = self.get_colors()
        wires = OpenGLVMobject()
        wires.start_new_path(np.array([2,0,-self.depth()])).add_line_to(np.array([2,1,-self.depth()]))
        wires.add_cubic_bezier_curve_to(np.array([2,1.8,-self.depth()]),np.array([2.8,2,-self.depth()]),np.array([4,2,-self.depth()]))
        wires.add_line_to(np.array([4,4,-self.depth()]))
        wires.start_new_path(np.array([4,0,-self.depth()]))
        wires.add_line_to(np.array([4,2,-self.depth()]))
        wires.start_new_path(np.array([6,0,-self.depth()]))
        wires.add_line_to(np.array([6,1,-self.depth()]))
        wires.add_cubic_bezier_curve_to(np.array([6,1.8,-self.depth()]),np.array([5.2,2,-self.depth()]),np.array([4,2,-self.depth()]))
        wires.set_stroke(color=C["generator_1_1"],width=5) # path_1_1
        return wires

    def get_wires_r1(self):
        C = self.get_colors()
        wires = OpenGLVMobject()
        wires.start_new_path(np.array([2,0,-2*self.depth()]))
        wires.add_line_to(np.array([2,3,-2*self.depth()]))
        wires.add_cubic_bezier_curve_to(np.array([2,3.8,-2*self.depth()]),np.array([2.6,4,-2*self.depth()]),np.array([3.5,4,-2*self.depth()]))
        wires.add_line_to(np.array([3.5,6,-2*self.depth()]))
        wires.start_new_path(np.array([4,0,-2*self.depth()]))
        wires.add_line_to(np.array([4,1,-2*self.depth()]))
        wires.add_cubic_bezier_curve_to(np.array([4,1.8,-2*self.depth()]),np.array([4.4,2,-2*self.depth()]),np.array([5,2,-2*self.depth()]))
        wires.add_line_to(np.array([5,3,-2*self.depth()]))
        wires.add_cubic_bezier_curve_to(np.array([5,3.8,-2*self.depth()]),np.array([4.4,4,-2*self.depth()]),np.array([3.5,4,-2*self.depth()]))
        wires.start_new_path(np.array([6,0,-2*self.depth()]))
        wires.add_line_to(np.array([6,1,-2*self.depth()]))
        wires.add_cubic_bezier_curve_to(np.array([6,1.8,-2*self.depth()]),np.array([5.6,2,-2*self.depth()]),np.array([5,2,-2*self.depth()]))
        wires.set_stroke(color=C["generator_1_1"],width=5) # path_1_1
        return wires

    # Points
    def get_points_r0(self):
        C = self.get_colors()
        points = []
        points.append(Circle(radius=0.125,color=C["generator_2_2"],fill_opacity=1).move_to(np.array([3,2,0]))) # circle_2_2
        points.append(Circle(radius=0.125,color=C["generator_2_2"],fill_opacity=1).move_to(np.array([4.5,4,0]))) # circle_2_2
        return points

    def get_points_s0(self):
        C = self.get_colors()
        points = []
        points.append(Circle(radius=0.125,color=C["generator_3_3"],fill_opacity=1).move_to(np.array([4,2,-self.depth()]))) # circle_3_3
        return points

    def get_points_r1(self):
        C = self.get_colors()
        points = []
        points.append(Circle(radius=0.125,color=C["generator_2_2"],fill_opacity=1).move_to(np.array([5,2,-2*self.depth()]))) # circle_2_2
        points.append(Circle(radius=0.125,color=C["generator_2_2"],fill_opacity=1).move_to(np.array([3.5,4,-2*self.depth()]))) # circle_2_2
        return points

    # We now put everything together
    def construct(self):
        r0_points = self.get_points_r0()
        s0_points = self.get_points_s0()
        r1_points = self.get_points_r1()

        r0 = VGroup(self.get_wires_r0(),*r0_points).shift(4*LEFT+3*DOWN)
        s0_wires = self.get_wires_s0()
        s0 = VGroup(s0_wires,*s0_points).shift(4*LEFT+3*DOWN)
        r1 = VGroup(self.get_wires_r1(),*r1_points).shift(4*LEFT+3*DOWN)
        f0_0 = Arrow(start=r0_points[0],end=s0_points[0])
        f0_1 = Arrow(start=r0_points[1],end=s0_points[0])
        f0 = VGroup(f0_0, f0_1)
        b0_0 = Arrow(start=r1_points[0],end=s0_points[0])
        b0_1 = Arrow(start=r1_points[1],end=s0_points[0])
        b0 = VGroup(b0_0, b0_1)

        self.play(Create(r0))

        self.play(self.camera.animate.rotate(60 * DEGREES, UP))
        self.play(self.camera.animate.move_to(np.array([0, 0, -self.depth()])))

        self.play(Create(r1))

        self.play(
            Create(f0_0), Create(f0_1),
            Create(s0_points[0]),
            Create(b0_0), Create(b0_1),
        )

        self.play(Create(s0_wires))

        text = MarkupText("Monoid associator", color=BLUE).next_to(s0, 2*UP)
        self.play(Write(text))
        # To play with the model interactively
        # self.interactive_embed()
        self.wait()

[NickHu]

https://docs.manim.community/en/stable/reference/manim.animation.movement.Homotopy.html
👀👀

[calintat]

Nice! Maybe we should have a 3D manim export as well.