A cubic in the neutral field with one tangent line riding it, plus the small rise-over-run triangle that makes the slope concrete. The loop drives the contact point out to each end of the curve and back in a single period, so the tangent visibly flattens through the turning points and the loop closes where it began.
manim/chasing_tangent.py
"""Chasing tangent: a tangent line sliding the length of a cubic.
Render (the driver does this for every palette; these are for eyeballing):
P=/opt/homebrew/opt/python@3.11/bin/python3.11
ASSET_MODE=still $P -m manim -s -t -r 1600,1600 manim/chasing_tangent.py ChasingTangent
ASSET_MODE=motion $P -m manim -qh -r 1600,1600 manim/chasing_tangent.py ChasingTangentLoop
"""
import numpy as np
from manim import (
DOWN,
LEFT,
TAU,
UP,
Dot,
Line,
The full Manim source and the rendered video come with a plan.
