Sierpinski Triangle¶

# Pascal's Triangle

N = 180
u = zeros(Int, N, N)
u[1, 1] = 1

# upper-left half
for i in 2:N # scan diagonally
    
    # boundary
    u[i, 1] = u[i-1, 1]
    u[1, i] = u[1, i-1]
    
    for j in 2:i-1
        u[j, i-j+1] = mod(u[j-1, i-j+1] + u[j, i-j], 2) # XOR
    end
end

# lower-right half
for i in 2:N
    for j in i:N
        u[j, N+i-j] = mod(u[j-1, N+i-j] + u[j, N+i-j-1], 2) # XOR
    end
end
        
img = Gray.(u)
#save("sier-pascal.png", img)

# Cellular automata (Rule 90)

N = 360
M = Int(N/2)
u = zeros(Int, M, N)
u[1, Int(N/2)] = 1 # sierpinski triangle
#u[1, :] .= rand(0:1, N) # random init

for i in 2:M
    
    u[i, 1] = mod(u[i-1, N] + u[i-1, 2], 2)
    u[i, N] = mod(u[i-1, N-1] + u[i-1, 1], 2)
    
    for j in 2:N-1
        u[i, j] = mod(u[i-1, j-1] + u[i-1, j+1], 2)
    end
end

img = Gray.(u)
#save("sier-rule90.png", img)