Lines and Art

Program inspired by the DES (Discrete Event Simulation) approach (in contract to continuous simulations that uses time_stepping).

Move with Reflection:

A line with a given starting position (px,py) and slope is drawn in a finite world. Collision on the walls will result in the change of slope of the line. examples:

1. [+m,+vy] -> wall(x=10) => [-m,+vy] A line with a positive gradient (+m) moving in the +vy direction -> hits the wall defined by x=10 => results in a line with a negative gradient(-m) and direction (-vy)

2. [+m,+vy] -> wall(y=10) => [-m,-vy] A line with a positive gradient (+m) moving in the +vy direction -> hits the wall defined by y=10 => results in a line with a negative gradient(-m) and direction (-vy)

3. [+m,-vy] -> wall(x=0) => [-m,-vy] A line with a positive gradient (+m) moving in the +vy direction -> hits the wall defined by x=0 => results in a line with a positive gradient(-m) and direction (-vy)

4. [+m,-vy] -> wall(y=0) => [-m,+vy] A line with a positive gradient (+m) moving in the +vy direction -> hits the wall defined by x=0 => results in a line with a positive gradient(-m) and direction (-vy)

Function Explanation:

default program ::: generates lines and their reflections are plotted from a given starting position (px,py) and a range of slopes [vf]

If done for many lines (or particles as they are called in the program) with given range of slopes, then the resulting plot is a fractal!

Video (YouTube)

With more engaging explanation.

Files

main_single_direction.py

px = 1   # starting posiiton in x
py = 0   # starting position in y
vx = 9   # x component of direction
vy = 8   # y component of direction
dirname = f"Plots_vx{vx}-vy{vy}_p{px}-{py}" # file name

gen_plot(particles, show_grid=True, show_color=False, line_width=1, pause_time=0.1,
         show_every_single_collision=True, save_every_single_collision=False,
                     show_final_plot=True,             save_final_plot=False,
         dots_per_in=200,
         folder_name=dirname)

create_video(dirname,video_name=f"Video_{dirname}",save_reverse_frames=False,frame_rate=5,max_range=[1, len(particles)])

px and py are the starting coordinates for the particle vx and vy are the starting direction for the particle

main_many_range.py

px = 0 # starting posiiton in x
py = 0 # starting position in y
slope_range = 21 # total range of gradients to take
dirname = f"Plots_rng{slope_range}_p{px}-{py}"

gen_plot(particles, show_grid=True, show_color=True,
         colors=["r","g","k"], line_width=0.1,
         show_wall_collision=False, show_final_plot=True, pause_time=0.1,
         save_wall_collision=False, save_final_plot=False, dots_per_in=200,
         folder_name=dirname)

Different arguments gen_plot() are used based on its use-case. gen_plot() will show and save the plots, the following arguments are briefed:

• show_color: assign color to the lines based on which corner it would end up when started from (px,py) = (0,0), the colors are red, green, and black
• color: allows to assign different colors to the lines
• line_width: set thickness of the lines
• show_every_single_collsion: recommended for single_direction, shows one collision per frame for one particle
• show_wall_collision: shows all wall collisions per frame for a single particle
• show_final_plot: show all collisions for all particles
• save_every_single_collsion: recommended for single_direction, save one collision per frame for one particle
• save_wall_collision: save all wall collisions per frame for a single particle
• save_final_plot: save all collisions for all particles
• pause_time: relevant when show_wall_collision or show_every_single_collision arguments are True, time interval between each frame to show
• dots_per_in: set dpi for saved plots

create_video(dirname,video_name=f"Video_{dirname}",save_reverse_frames=False,frame_rate=5, max_range=[1, len(particles)])

create_video() generates a video of the saved frames from gen_plot()

• save_reverse_frames: creates a copy of all the frames in reverse order
• frame_rate: set frames per second
• max_range: determines the max number of frames (including the reverse), it is used as a preventive measure for it not produce any more frames than necessary