Module:Ulam spiral
Τεκμηρίωση module[δημιουργία] [ανανέωση]
-- Generate Ulam spiral based on primes, fibonacci, triangular numbers etc.
-- Gts@el wiki, Sep. 2017
local p = {}
-- determine whether number is prime
-- params: n (number)
-- return: boolean
local function is_prime(n)
for i = 2, n^(1/2) do
if (n % i) == 0 then
return false
end
end
return true
end
-- determine whether number is triangular
-- params: n (number)
-- return: boolean
local function is_triangular(n)
x = (math.sqrt(8*n + 1) - 1) / 2
return (x % 1 == 0)
end
-- determine whether number is part of standard fibonacci sequence
-- params: n (number)
-- return: boolean
local function is_fib(n)
if n == 0 then
return true
end
phi = 0.5 + (0.5 * math.sqrt(5.0))
a = phi * n
return math.abs(math.floor(a+0.5) - a) < 1.0 / n
end
-- determine total divisors of a number
-- params: n (number)
-- return: int
local function divisors(n)
limit = n;
total = 0;
if n == 1 then
return 1
end
for i = 1, limit-1 do
if n % i == 0 then
limit = n / i
if limit ~= i then
total = total + 1
end
total = total + 1
end
end
return total
end
-- CSS border for cells in order to recreate spiral
-- params: row (number), column (number), size (number)
-- return string
function border(row, column, size)
local on = 'solid '
local top, left, right, bottom = 'none ', 'none ', 'none ', 'none '
local last = size - 1
if column == math.floor(size/2) and row == column then
bottom = on
elseif row == math.floor(size/2) and column==row+1 then
bottom=on
right=on
end
if row < column and column < last - row then
bottom = on
elseif row > column and row < last - column then
right = on
elseif row >= column-1 and row < last and row > size/2 then
bottom = on
if column == row + 1 and column < last then
right = on
end
elseif column>row and column < last then
right = on
end
result = top .. right .. bottom .. left
result = result:gsub("%s$", "")
return result
end
-- convert values to wikitable. The wikitable string is preproccessed in frame.
-- params: data (dictionary), size (int), fontSize (int)
-- return: string object
local function wikitable(data, size, fontSize)
local fontSize = '0.9' --em
if tonumber(size) > 10 and tonumber(size) <=30 then
fontSize = '0.8'
elseif tonumber(size) > 30 and tonumber(size) <= 50 then
fontSize = '0.6'
elseif tonumber(size) > 50 then
fontSize = '0.3'
end
local result = '{| style="font-size:' .. fontSize .. 'em;text-align:center;border-spacing:0px"'
-- background colour of a number corresponding to number of divisors
divi = {
[2] = 'lightskyblue',
[3] = '#86f99f',
[4] = '',
[5] = '',
[6] = '',
[7] = '',
[8] = '',
[9] = '',
}
-- create wikitable
for row=0, size-1 do
result = result .. '\n|-\n|'
for column=0, size-1 do
if column > 0 then
result = result .. '||'
end
number = data[row .. ':' .. column]
bgcolor =''
divtotal = divisors(number)
if divtotal > 60 then
bgcolor = '#f98686'
else
bgcolor = tostring(divi[divtotal])
end
result = result .. 'title="' .. math.floor(number) .. '" style="border-color:#adadad;border-size:1px;border-style:' .. border(row, column, size) .. ';background-color:'.. bgcolor .. ';color:black"|'
--result = result .. 'title="' .. math.floor(number) .. '" style="border-radius:50%;background-color:'.. bgcolor .. ';color:black !important"|'
number = math.floor(data[row .. ':' .. column])
--if bgcolor ~= '' and bgcolor ~= 'nil' then
if number <= tonumber(os.date('%Y')) then
result = result .. '[[' .. number .. ' (αριθμός)|' .. number .. ']]'
else
result = result .. number
end
--else
-- result = result .. number
--end
end
end
result = result .. '\n|}'
-- preprocess string in frame and render table
local frame = mw.getCurrentFrame()
result = frame:preprocess(result)
return result
end
-- calculate ulam spiral value for each x,y tabular point.
-- algorithm concept based on Python version at GPL 3 https://rosettacode.org/wiki/Ulam_spiral_(for_primes)#Python
-- use of bitwise ops was attempted but Mediawiki Scribunto Lua doesn't seem to like them
-- params: n (int), x (int), y (int), start (int)
-- return: int
local function cell(n, x, y, start)
local d = 0
local x = x - math.floor((n - 1) /2)
local y = y - math.floor(n / 2)
l = 2 * math.max(math.abs(x), math.abs(y))
if y <= x then
d = (l*3) + x + y
else
d = l - x - y
end
return math.pow(l - 1, 2) + d + start - 1
end
-- prepare spiral display for output type (i.e. wikitable, coords only, etc)
-- params: size (int), start (int)
-- return: mixed
local function show_spiral(size, start)
local result = {}
for i=0, size-1 do
for x=0, i do
for y=0, i do
result[x .. ':' .. y] = cell(size, x, y, start)
end
end
end
return wikitable(result, size)
end
-- main
-- params: frame
-- return: mixed
function p.ulam(frame)
local size = tonumber(frame.args[1])
local start = tonumber(frame.args[2])
if size > 70 then
return 'Το ανώτατο επιτρεπτό όριο διαστάσεων πίνακα είναι 70x70'
end
return show_spiral(size, start)
end
return p