\phi = (cos(\omega t + \delta), sin(\omega t + \delta), k ~ \delta, 0) \, \textrm{with} \, \delta: 0 \to 10 \pi
\textrm{red} = (cos(\delta), sin(\delta), k ~ \delta, 0) \, \textrm{with} \, \delta: 0 \to 10 \pi

q_graph -out amp_shifted_marked -dir int14 -box 1.6 -command 't_function -t_func cos -x_func sin -y_func zero -z_func zero -n_steps 0 -pi 10 -n_t_cycles 1000 -n_t_step 0.0314 1 1 0 0 | q_add 0 0 -1.5 -.1 | q_add_n_m 0 0 0.003 0 1 1000' -color red -command 't_function -t_func cos -x_func sin -y_func zero -z_func zero -n_steps 1000 -pi 10 -n_t_cycles 1000 -n_t_step 0.0314 1 1 0 0 | q_add 0 0 -1.5 0 | q_add_n_m 0 0 0.003 0 1000 1000' -color yellow

\phi'^* \phi = (cos(\omega t + \delta), 0, -sin(\omega t + \delta), 0)(cos(\omega t), 0, sin(\omega t), 0) + (0, k \delta, 0, 0) \, \textrm{with} \, \delta: 0 \to 10 \pi in red
\phi^* \phi'= (cos(\omega t), 0, -sin(\omega t), 0)(cos(\omega t + \delta), 0,  sin(\omega t + \delta), 0) + (0, k \delta, 0, 0) \, \textrm{with} \, \delta: 0 \to 10 \pi in blue

q_graph -out interference_ty_red_blue -dir int14 -box 1.6 -command '221 "t_function -t_function cos -x_function zero -y_function sin -z_function zero -n_step 1799 -pi 124 -n_t_cycles 1000 -n_t_step 0 1 0 1 0 | q_conj" "t_function -t_function cos -x_function zero -y_function sin -z_function zero -n_step 1799 -pi 124 -n_t_cycles 1000 -n_t_step 0.031 1 0 1 0" | q_x | q_add 0 -1.5 0 0 | q_add_n_m 0 0.003 0 0 1800 1000' -color red -command '221 "t_function -t_function cos -x_function zero -y_function sin -z_function zero -n_step 1799 -pi 124 -n_t_cycles 1000 -n_t_step 0.031 1 0 1 0 | q_conj" "t_function -t_function cos -x_function zero -y_function sin -z_function zero -n_step 1799 -pi 124 -n_t_cycles 1000 -n_t_step 0 1 0 1 0" | q_x | q_add 0 -1.5 0 0 | q_add_n_m 0 0.003 0 0 1800 1000' -color blue

(t, x, y, z) = (t, cos (2 t + 3), 0, 0)

q_graph -out sho-x -dir sho -box 10 -command 't_function -mqs 2 -mqs 1 -t_function polynomial -t_function one -x_function cos -x_function polynomial -y_function zero -y_function zero -z_function zero -z_function zero 1 2 1 2 1 3 0 0 0 1 0 0 -shift "-11 5 0 0" -pi 8 -n_steps 1600' -color yellow

(t, x, y, z) = (t, cos( 2 t + 3), 0, 0)
(\gamma, \gamma \beta_x, \gamma \beta_y, \gamma \beta_z) = (1, -2 sin( 2 t + 3), 0, 0)

q_graph -out sho-x_and_v -dir sho -box 10 -command 't_function -mqs 2 -mqs 1 -t_function polynomial -t_function one -x_function cos -x_function polynomial -y_function zero -y_function zero -z_function zero -z_function zero 1 2 1 2 1 3 0 0 0 1 0 0 -shift "-11 5 0 0" -pi 8 -n_steps 1600' -color yellow -command 't_function -mqs 2 -mqs 1 -t_function one -t_function one -x_function sin -x_function polynomial -y_function zero -y_function zero -z_function zero -z_function zero -shift "0 5 0 0" -pi 8 -n_steps 1600 -- 1 2 1 2 1 3 0 0 0 -2 0 0' -color blue

(t, x, y, z) = (t, cos(2 t + 3), 0, 0)
(\gamma, \gamma \beta_x, \gamma \beta_y, \gamma \beta_z) = (1, -2 sin(2 t + 3, 0, 0)
(a_t, a_x, a_y, a_z) = (0, -4 cos(2 t + 3, 0, 0)

q_graph -out sho-x_and_v_and_a -dir sho -box 10 -command 't_function -mqs 2 -mqs 1 -t_function polynomial -t_function one -x_function cos -x_function polynomial -y_function zero -y_function zero -z_function zero -z_function zero 1 2 1 2 1 3 0 0 0 1 0 0 -shift "-11 5 0 0" -pi 8 -n_steps 1600' -color yellow -command 't_function -mqs 2 -mqs 1 -t_function one -t_function one -x_function sin -x_function polynomial -y_function zero -y_function zero -z_function zero -z_function zero -shift "0 5 0 0" -pi 8 -n_steps 1600 -- 1 2 1 2 1 3 0 0 0 -2 0 0' -color blue -command 't_function -mqs 2 -mqs 1 -t_function zero -t_function zero -x_function cos -x_function polynomial -y_function zero -y_function zero -z_function zero -z_function zero -shift "0 5 0 0" -pi 8 -n_steps 1600 -- 1 2 1 2 1 3 0 0 0 -4 0 0' -color red

(t, x, y, z) = (t, cos(2 t + 3), 6 cos(t + 2), 8 cos(t/2 + 1))
(\gamma, \gamma \beta_x, \gamma \beta_y, \gamma \beta_z) = (1, -2 sin(2 t + 3), -6 sin(t + 2), -4 sin(t/2 + 1))
(a_t, a_x, a_y, a_z) = (0, -4 cos(2 t + 3), -6 cos(t + 2), -2 cos(t/2 + 1))

q_graph -out sho-xyz_and_v_and_a -dir sho -box 10 -command 't_function -mqs 2 -mqs 1 -t_function polynomial -t_function one -x_function cos -x_function polynomial -y_function cos -y_function polynomial -z_function cos -z_function polynomial 1 2 1 2 1 3 2 1 0 1 6 8 -shift "-11 5 0 0" -pi 8 -n_steps 1600' -color yellow -command 't_function -mqs 2 -mqs 1 -t_function one -t_function one -x_function sin -x_function polynomial -y_function sin -y_function polynomial -z_function sin -z_function polynomial -shift "0 5 0 0" -pi 8 -n_steps 1600 -- 1 2 1 2 1 3 2 1 0 -2 -6 -4' -color blue -command 't_function -mqs 2 -mqs 1 -t_function zero -t_function zero -x_function cos -x_function polynomial -y_function cos -y_function polynomial -z_function cos -z_function polynomial -shift "0 5 0 0" -pi 8 -n_steps 1600 -- 1 2 1 2 1 3 2 1 0 -4 -6 -2' -color red

Triangle:
(0, 0, 0, 0), (1, 0, 0, 0), and (1, -.7, -2, 0)
Circle:
Center: (0, 0, 0, 0)
Intersects: (1, -.7, -2, 0)

./q_graph -box 1.3 -dir triangles -out timelike_future -command 'g_u1_n 1 -.7 -.2 0 2000 | q_x_scalar 1.23693' -color green -command 'constant_linear_motion 100 0 0 0 0 1 0 0 0' -color red -command 'constant_linear_motion 100 0 0 0 0 1 -.7 -.2 0' -color blue -command 'constant_linear_motion 100 1 0 0 0 1 -.7 -.2 0' -color yellow

Triangle formed between events: (0, 0, 0, 0), (-1, 0, 0, 0), and (-1, 0.7, 0, 0)

./q_graph -box 1.3 -dir triangles -out timelike_past -command 'g_u1_n -1 .7 .2 0 2000 | q_x_scalar 1.23693' -color green -command 'constant_linear_motion 100 0 0 0 0 -1 0 0 0' -color red -command 'constant_linear_motion 100 0 0 0 0 -1 .7 .2 0' -color blue -command 'constant_linear_motion 100 -1 0 0 0 -1 .7 .2 0' -color yellow

Triangle between events: (0, 0, 0, 0), (0, 1, 0, 0), and (0.7, 0, 0, 0)

./q_graph -box 1.3 -dir triangles -out spacelike_right -command 'g_u1_n 0.53 0.7 .2 0 2000 | q_x_scalar 1.23693' -color green -command 'constant_linear_motion 100 0 0.961522 0.274720 0 0.728009 0.961522 0.274720 0' -color purple -command 'constant_linear_motion 100 0 0 0 0 0.728009 0.961522 0.274720 0' -color blue -command 'constant_linear_motion 100 0 0 0 0 0 0.961522 0.274720 0' -color yellow

4 triangles:
(0, 0, 0, 0), ( 1, 0, 0, 0), ( 1,-0.7,-0.2, 0)
(0, 0, 0, 0), (-1, 0, 0, 0), (-1, 0.7, 0.2, 0)
(0, 0, 0, 0), (0, 0.961, 0.274, 0), ( 0.728, 0.961, 0.274, 0)
(0, 0, 0, 0), (0,-0.961,-0.274, 0), (-0.728,-0.961,-0.274, 0)

./q_graph -box 1.3 -dir triangles -out t4 -command 'g_u1_n -1 .7 .2 0 2000 | q_x_scalar 1.23693' -color green -command 'constant_linear_motion 100 0 0 0 0 -1 0 0 0' -color red -command 'constant_linear_motion 100 0 0 0 0 -1 .7 .2 0' -color blue -command 'constant_linear_motion 100 -1 0 0 0 -1 .7 .2 0' -color yellow -command 'constant_linear_motion 100 0 0 0 0 1 0 0 0' -color red -command 'constant_linear_motion 100 0 0 0 0 1 -.7 -.2 0' -color blue -command 'constant_linear_motion 100 1 0 0 0 1 -.7 -.2 0' -color yellow -command 'constant_linear_motion 100 0 0.961522 0.274720 0 0.728009 0.961522 0.274720 0' -color purple -command 'constant_linear_motion 100 0 0 0 0 0.728009 0.961522 0.274720 0' -color blue -command 'constant_linear_motion 100 0 0 0 0 0 0.961522 0.274720 0' -color yellow -command 'constant_linear_motion 100 0 -0.961522 -0.274720 0 -0.728009 -0.961522 -0.274720 0' -color purple -command 'constant_linear_motion 100 0 0 0 0 -0.728009 -0.961522 -0.274720 0' -color blue -command 'constant_linear_motion 100 0 0 0 0 0 -0.961522 -0.274720 0' -color yellow


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