How can I sweep through variables to show what changing them does to a graph?

[remusco]

This is a beginner question, but I'm struggling with this.
I have an equation that represents the temperature distribution along one dimension:

I would like to plot the temperature as a function of the distance x. I want to display all the other parameters on the screen (T_l, T_r, q, K, L) and sweep through the parameters (one at a time) to show what the curve does when these parameters change. I want to display the parameter value on the screen and constantly have this update.
Can someone walk me through the easiest way to do this?
Here is what I have so far:

from manim import *
pixel_width = 450
pixel_height = 800

config.frame_width=20
config.frame_height=15



class TemperatureDistribution(Scene):
    def construct(self):
        # initialize the parameter values
        T_l_init = 300  # Left temperature (in Kelvin)
        T_r_init = 400  # Right temperature (in Kelvin)
        q_init = 100    # Heat generation rate (W/m^3)
        k_init = 50     # Thermal conductivity (W/m·K)
        L_init = 10     # Length of the rod (meters)
        
        
        # Define the temperature function T(x)
        def T(x,T_l,T_r,q,k,L):
            return T_l+(0.5*(L**2)*(q/k)+T_r-T_l)*(x/L)-(0.5*L**2)*(q/k)*(x/L)**2

        axes = Axes(
            x_range=[0, 10,1],
            y_range=[200, 1000 + 50,50],
            axis_config={"include_numbers": True},
        )

        x_label = axes.get_x_axis_label("distance, x [m]")  # Label for the x-axis
        y_label = axes.get_y_axis_label("Temperature, T(x) [K]")  # Label for the y-axis
        
        # Create the graph of the temperature distribution function T(x)
        graph = axes.plot(lambda x: T(x,T_l_init,T_r_init,q_init,k_init,L_init))
        
        # Label the axes
        # Add the axes and the graph to the scene
        self.play(Create(axes))
        self.play(Create(graph))
        self.play(Write(x_label), Write(y_label))
        # Animate the graph by changing the value of L (length of the rod)
    
        label1=MathTex(f'T_l={T_l_init}')
        label1.shift(5*UP+3*RIGHT)
        
        label2=MathTex(f'T_r={T_r_init}')
        label2.next_to(label1,DOWN)
        
        label3=MathTex(f'q={q_init}')
        label3.next_to(label2,DOWN)

        label4=MathTex(f'k={k_init}')
        label4.next_to(label3,DOWN)

        label5=MathTex(f'L={L_init}')
        label5.next_to(label4,DOWN)


        self.play(Write(label1))
        self.play(Write(label2))
        self.play(Write(label3))
        self.play(Write(label4)) 
        self.play(Write(label5))
        self.wait(2)

[paarthsiloiya]

Use the ValueTracker() and updaters. Here is the code

#https://github.com/ManimCommunity/manim/discussions/4139#discussion-7877358

from manim import *
pixel_width = 450
pixel_height = 800

config.frame_width=20
config.frame_height=15



class TemperatureDistribution(Scene):
    def construct(self):
        # initialize the parameter value trackers
        T_l = ValueTracker(300)  # Left temperature (in Kelvin)
        T_r = ValueTracker(400)  # Right temperature (in Kelvin)
        q = ValueTracker(100)    # Heat generation rate (W/m^3)
        k = ValueTracker(50)     # Thermal conductivity (W/m·K)
        L = ValueTracker(10)     # Length of the rod (meters)
        
        
        # Define the temperature function T(x)
        def T(x,T_l,T_r,q,k,L):
            return T_l+(0.5*(L**2)*(q/k)+T_r-T_l)*(x/L)-(0.5*L**2)*(q/k)*(x/L)**2

        axes = Axes(
            x_range=[0, 10, 1],
            y_range=[0, 700 ,50],
            axis_config={"include_numbers": True},
        )

        x_label = axes.get_x_axis_label("distance, x [m]")  # Label for the x-axis
        y_label = axes.get_y_axis_label("Temperature, T(x) [K]")  # Label for the y-axis
        
        # Create the graph of the temperature distribution function T(x)
        graph = axes.plot(lambda x: T(x,T_l.get_value(),T_r.get_value(),q.get_value(),k.get_value(),L.get_value()))

        graph.add_updater(
            lambda m : m.become(
                axes.plot(lambda x: T(x,T_l.get_value(),T_r.get_value(),q.get_value(),k.get_value(),L.get_value()))
            )
        )
        
        # Label the axes
        # Add the axes and the graph to the scene
        self.play(Create(axes))
        self.play(Create(graph))
        self.play(Write(x_label), Write(y_label))
        # Animate the graph by changing the value of L (length of the rod)
    
        T_l_label = DecimalNumber(T_l.get_value(), num_decimal_places=3)
        T_r_label = DecimalNumber(T_r.get_value(), num_decimal_places=3)
        q_label = DecimalNumber(q.get_value(), num_decimal_places=3)
        k_label = DecimalNumber(k.get_value(), num_decimal_places=3)
        L_label = DecimalNumber(L.get_value(), num_decimal_places=3)

        T_l_label.add_updater(lambda m: m.set_value(T_l.get_value()))
        T_r_label.add_updater(lambda m: m.set_value(T_r.get_value()))
        q_label.add_updater(lambda m: m.set_value(q.get_value()))
        k_label.add_updater(lambda m: m.set_value(k.get_value()))
        L_label.add_updater(lambda m: m.set_value(L.get_value()))
        
        parameters = VGroup(
            VGroup(MathTex("T_l = "), T_l_label).arrange(RIGHT),
            VGroup(MathTex("T_r = "), T_r_label).arrange(RIGHT),
            VGroup(MathTex("q = "), q_label).arrange(RIGHT),
            VGroup(MathTex("k = "), k_label).arrange(RIGHT),
            VGroup(MathTex("L = "), L_label).arrange(RIGHT)
        ).arrange(DOWN, aligned_edge=LEFT).to_corner(UR, buff=2)

        self.play(
            Create(parameters)
        )


        # Animate the parameters
        self.play(
            T_l.animate.set_value(500)
        )
        self.play(
            T_l.animate.set_value(100)
        )
        self.play(
            T_l.animate.set_value(300)
        )

And here is the result

TemperatureDistribution.mp4