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All functions

broadcast_black_pixel()
Broadcast Black Pixel Update
broadcast_update()
Broadcast Grid Update to Workers
check_termination()
Check Walker Termination Conditions
cleanup_async()
Clean Up Async Resources
close_sockets()
Close Sockets
count_black_pixels()
Count Black Pixels in Grid
create_controller()
Create Async Controller (Auto-detect Backend)
create_pub_socket()
Create Nanonext Publisher Socket
create_walker()
Create a Walker
find_isolated_pixels()
Find Isolated Pixels in Grid
format_statistics()
Format Simulation Statistics for Display
generate_walker_positions()
Generate Random Starting Positions for Walkers
get_black_percentage()
Get Percentage of Black Pixels
get_neighbors()
Get Neighboring Positions
get_neighbors_bounded()
Get Neighbor Positions (Bounded)
get_pixel()
Get Pixel Value from Grid
has_black_neighbor()
Check if Walker Has Black Neighbor
init_publisher_socket()
Initialize Publisher Socket
init_subscriber_socket()
Initialize Subscriber Socket
initialize_grid()
Initialize a Grid
is_within_bounds()
Check if a Position is Within Grid Bounds
plot_grid() plot(<randomwalk_result>)
Plot Final Grid State
plot_grid_enhanced()
Enhanced Grid Plot with Arrival Time Coloring
plot_simulation()
Plot Simulation Results
plot_walker_paths()
Plot Walker Paths
print_simulation_result()
Print Simulation Result
run_dashboard()
Run Shiny Dashboard App
run_simulation()
Run a Random Walk Simulation
set_pixel_black()
Set Pixel Value in Grid
sim_input_server()
Simulation Input Module Server
sim_input_ui()
Simulation Input Module UI
sim_output_server()
Simulation Output Module Server
sim_output_ui()
Simulation Output Module UI
simulate_walker_dynamic()
Simulate Walker with Dynamic Grid Broadcasting
step_walker()
Move Walker One Step
touches_black()
Check if Walker Touches a Black Pixel
update_grid_from_broadcasts()
Update Local Grid from Broadcasts
validate_no_isolated_pixels()
Validate Grid State for Isolated Pixels
validate_termination_position()
Validate Termination Position
worker_check_updates()
Check for Grid Updates (Worker)
worker_init()
Initialize Worker with Subscriber Socket
worker_run_walker()
Run Walker Until Termination (Worker Task)
worker_step_walker()
Execute Walker Step (Worker)
wrap_position()
Wrap Position Around Grid Boundaries (Torus Topology)