How to create a better 3D Discrete Plot?

I am study the Discrete Klein-Gordon Equation.

By interpreting the equation in this way, we can relate the dynamics described by the discrete Klein - Gordon equation to the behavior of DNA molecules within a biological system . This analogy allows us to understand the behavior of DNA in terms of concepts from physics and mathematical modeling . Is ti possivle to I create a nicer 3D plot than the following?

% Parameters
numBases = 100; % Number of base pairs
kappa = 0.1; % Elasticity constant
omegaD = 0.2; % Frequency term
beta = 0.05; % Nonlinearity coefficient

% Initial conditions
initialPositions = 0.01 + (0.02 - 0.01) * rand(numBases, 1);
initialVelocities = zeros(numBases, 1);

% Time span for the simulation
tSpan = [0 50];

% Differential equations function
odeFunc = @(t, y) [y(numBases+1:end); ... % velocities
                   kappa * ([y(2); y(3:numBases); 0] - 2 * y(1:numBases) + [0; y(1:numBases-1)]) + ...
                   omegaD^2 * (y(1:numBases) - beta * y(1:numBases).^3)]; % accelerations

% Solve the system numerically
[T, Y] = ode45(odeFunc, tSpan, [initialPositions; initialVelocities]);

% Specific time points for visualization
timePoints = [0, 10, 20, 30, 40, 50];

% Initialize the figure for 3D plot
figure;
hold on;

% Plotting the dynamics in 3D
for i = 1:length(timePoints)
    time = timePoints(i);
    [~, timeIndex] = min(abs(T - time));  % Find the index of the closest time in T
    displacements = Y(timeIndex, 1:numBases);  % Displacement values at this time point

    % Plotting each base pair displacement as a line in 3D space
    plot3(1:numBases, repmat(time, 1, numBases), displacements, 'LineWidth', 2);
end

hold off;
xlabel('Base Pair');
ylabel('Time');
zlabel('Displacement');
title('3D Plot of DNA Base Pair Displacements Over Time');
view(3); % Adjust the view to see the plot in 3D

Answer 1

[Voss]

Maybe a surface? Something like this:

% Parameters
numBases = 100; % Number of base pairs
kappa = 0.1; % Elasticity constant
omegaD = 0.2; % Frequency term
beta = 0.05; % Nonlinearity coefficient

% Initial conditions
initialPositions = 0.01 + (0.02 - 0.01) * rand(numBases, 1);
initialVelocities = zeros(numBases, 1);

% Time span for the simulation
tSpan = [0 50];

% Differential equations function
odeFunc = @(t, y) [y(numBases+1:end); ... % velocities
                   kappa * ([y(2); y(3:numBases); 0] - 2 * y(1:numBases) + [0; y(1:numBases-1)]) + ...
                   omegaD^2 * (y(1:numBases) - beta * y(1:numBases).^3)]; % accelerations

% Solve the system numerically
[T, Y] = ode45(odeFunc, tSpan, [initialPositions; initialVelocities]);

% Specific time points for visualization
timePoints = [0, 10, 20, 30, 40, 50];

% Initialize the figure for 3D plot
figure;

% Plotting the dynamics in 3D
[~, timeIndex] = min(abs(T - timePoints),[],1);  % Find the index of the closest time in T

surf(1:numBases, repmat(timePoints(:), 1, numBases), Y(timeIndex, 1:numBases), ...
    'EdgeColor', 'none', 'FaceColor', 'interp')

box on;
xlabel('Base Pair');
ylabel('Time');
zlabel('Displacement');
title('3D Plot of DNA Base Pair Displacements Over Time');
view(3); % Adjust the view to see the plot in 3D

[Voss]

Or a mesh:

% Parameters
numBases = 100; % Number of base pairs
kappa = 0.1; % Elasticity constant
omegaD = 0.2; % Frequency term
beta = 0.05; % Nonlinearity coefficient

% Initial conditions
initialPositions = 0.01 + (0.02 - 0.01) * rand(numBases, 1);
initialVelocities = zeros(numBases, 1);

% Time span for the simulation
tSpan = [0 50];

% Differential equations function
odeFunc = @(t, y) [y(numBases+1:end); ... % velocities
                   kappa * ([y(2); y(3:numBases); 0] - 2 * y(1:numBases) + [0; y(1:numBases-1)]) + ...
                   omegaD^2 * (y(1:numBases) - beta * y(1:numBases).^3)]; % accelerations

% Solve the system numerically
[T, Y] = ode45(odeFunc, tSpan, [initialPositions; initialVelocities]);

% Specific time points for visualization
timePoints = [0, 10, 20, 30, 40, 50];

% Initialize the figure for 3D plot
figure;

% Plotting the dynamics in 3D
[~, timeIndex] = min(abs(T - timePoints),[],1);  % Find the index of the closest time in T

mesh(1:numBases, repmat(timePoints(:), 1, numBases), Y(timeIndex, 1:numBases))

box on;
xlabel('Base Pair');
ylabel('Time');
zlabel('Displacement');
title('3D Plot of DNA Base Pair Displacements Over Time');
view(3); % Adjust the view to see the plot in 3D

[Voss]

Or a waterfall plot:

% Parameters
numBases = 100; % Number of base pairs
kappa = 0.1; % Elasticity constant
omegaD = 0.2; % Frequency term
beta = 0.05; % Nonlinearity coefficient

% Initial conditions
initialPositions = 0.01 + (0.02 - 0.01) * rand(numBases, 1);
initialVelocities = zeros(numBases, 1);

% Time span for the simulation
tSpan = [0 50];

% Differential equations function
odeFunc = @(t, y) [y(numBases+1:end); ... % velocities
                   kappa * ([y(2); y(3:numBases); 0] - 2 * y(1:numBases) + [0; y(1:numBases-1)]) + ...
                   omegaD^2 * (y(1:numBases) - beta * y(1:numBases).^3)]; % accelerations

% Solve the system numerically
[T, Y] = ode45(odeFunc, tSpan, [initialPositions; initialVelocities]);

% Specific time points for visualization
timePoints = [0, 10, 20, 30, 40, 50];

% Initialize the figure for 3D plot
figure;

% Plotting the dynamics in 3D
[~, timeIndex] = min(abs(T - timePoints),[],1);  % Find the index of the closest time in T

waterfall( ...
    repmat(1:numBases, numel(timePoints), 1), ...
    repmat(timePoints(:), 1, numBases), ...
    Y(timeIndex, 1:numBases))

box on;
xlabel('Base Pair');
ylabel('Time');
zlabel('Displacement');
title('3D Plot of DNA Base Pair Displacements Over Time');
view(3); % Adjust the view to see the plot in 3D

[Athanasios Paraskevopoulos]

Thank you very much for your help and your time!!!

[Voss]

You're welcome!