use 'math'
use 'graph'
use 'iter'
local function c_generator(n, n_angle, len_frac, g)
 local exp, real, imag = complex.exp, complex.real, complex.imag
 local w, r, k = ilist(|| 0, n+1), #g
 local s = len_frac^n
 local sz = matrix.cnew(n_angle, 1, |k| s * exp(2i*pi*(k-1)/n_angle))
 local sh = ilist(|k| g[(k-1)%r+1] - g[(k-2)%r+1], r)
 local a = (g[1]*n) % n_angle
 local z = 0
 return function()
	 if w[n+1] == 0 then
		local j
		z = z + sz[a+1]
		for j=1,n+1 do
		 w[j] = (w[j] + 1) % r
		 a = (a + sh[w[j]+1]) % n_angle
		 if w[j] ~= 0 then
		 break
		 end
		end
		return real(z), imag(z)
	 end
	 end
end
local function levyc(n)
 local p = plot('Levy\'s C curve')
 local c = ipath(c_generator(n, 4, 1/2, {-1,0,0,1}))
 p:addline(c, 'red', {}, {{'rotate', angle= -pi/4}})
 p:addline(c, 'red', {}, {{'translate', x=1/sqrt(2), y=-1/sqrt(2)},{'rotate', angle= pi/4}})
 p.units = false
 p:show()
 return p
end
local function von_koch_demo() 
 local pl = plot()
 local t = path()
 t:move_to(0,0)
 t:line_to(1,0)
 t:line_to(0.5,-sqrt(3)/2)
 t:close()
 local v = ipath(c_generator(4, 6, 1/3, {0,1,-1,0}))
 local c = rgba(0,0,180,50)
 pl:add(v, c)
 pl:add(v, c, {}, {{'translate', x=1, y=0}, {'rotate', angle=-2*pi/3}})
 pl:add(v, c, {}, {{'translate', x=0.5, y=-sqrt(3)/2}, 
		 {'rotate', angle=-2*2*pi/3}})
 pl:add(t, c)
 c = rgb(0,0,180)
 pl:addline(v, c)
 pl:addline(v, c, {}, {{'translate', x=1, y=0}, {'rotate', angle=-2*pi/3}})
 pl:addline(v, c, {}, {{'translate', x=0.5, y=-sqrt(3)/2}, 
			 {'rotate', angle=-2*2*pi/3}})
 pl.units = false
 pl:show()
end
local levy_curve_demo = function(n) return levyc(n and n or 6) end 
local function pitag_tree_symm_demo()
 local rdsd = sqrt(2)/2
 local ubox = rect(0, 0, 1, 1)
 local cf
 local function pitag_tree(pl, x, y, th, ll, depth)
 local col = cf(depth)
 pl:add(ubox, col, {}, {{'translate', x= x, y= y}, 
			 {'rotate', angle= th}, 
			 {'scale', ll}})
 if depth> 0 then
	 x, y = x - ll*sin(th), y + ll*cos(th)
	 pitag_tree(pl, x, y, th + pi/4, ll*rdsd, depth-1)
	 x, y = x + ll*rdsd*cos(th+pi/4), y + ll*rdsd*sin(th+pi/4)
	 pitag_tree(pl, x, y, th - pi/4, ll*rdsd, depth-1)
 end
 end
 local depth = 12
 local cfgen = color_function('darkgreen', 255)
 cf = |d| cfgen(1-d/depth)
 local pl = plot()
 pl.units = false
 pitag_tree(pl, 0, 0, 0, 1, depth)
 pl:show()
end
local function pitag_tree_demo(n)
 local ubox = rect(0, 0, 1, 1)
 n = n and n or 10
 local col, coln
 local function pitag_tree(pl, x, y, th, ll, depth)
 if depth == 0 then
	 local tr = {{'translate', x= x, y= y}, {'rotate', angle= th}, 
		 {'scale', ll}}
	 pl:add(ubox, col, {}, tr)
	 pl:add(ubox, coln, {{'stroke', width= 2.5*ll}}, tr)
 end
 if depth> 0 then
	 x, y = x - ll*sin(th), y + ll*cos(th)
	 local a1 = th + atan2(12,16)
	 pitag_tree(pl, x, y, a1, ll*4/5, depth-1)
	 x, y = x + ll*4/5*cos(a1), y + ll*4/5*sin(a1)
	 pitag_tree(pl, x, y, th + atan2(-12,9), ll*3/5, depth-1)
 end
 end
 local cfgen = color_function('darkgreen', 255)
 local pl = plot()
 pl.sync = false
 pl.clip = false
 pl:show()
 for k=0, n do
 col, coln = cfgen(k/n), cfgen((k+1)/n)
 pitag_tree(pl, 0, 0, 0, 1, k)
 pl:flush()
 end
end
return {'Fractals', {
 {
 name = 'vonkoch',
 f = von_koch_demo, 
 description = 'Von Koch\'s curve',
 },
 {
 name = 'levyc',
 f = levy_curve_demo, 
 description = 'Levy\'s C curve',
 },
 {
 name = 'pitags',
 f = pitag_tree_symm_demo, 
 description = 'Pythagorean Tree (symmetric)',
 },
 {
 name = 'pitaga',
 f = pitag_tree_demo, 
 description = 'Pythagorean Tree (asymmetric)',
 },
}}
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