initial commit

README.md

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+# Fractals in Love2D
+
+```sh
+love .
+```
+
+Available fractals:
+* Sierpiński triangle
+* Circles

Vector2.lua

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+local ffi = assert(require("ffi"), "Vector2 needs ffi to be enabled")
+local Vector2 = {}
+setmetatable(Vector2, Vector2)
+
+ffi.cdef[[
+typedef struct {
+  double x, y;
+} vector2;
+]]
+
+function Vector2.copy(t)
+  return ffi.new("vector2", t.x, t.y)
+end
+
+function Vector2.__call(t, x, y)
+  return ffi.new("vector2", x or 0, y or 0)
+end
+
+function Vector2.__concat(v1, v2)
+  return v1 .. tostring(v2)
+end
+
+function Vector2.__tostring(t)
+  return ffi.istype("vector2", t) and string.format("Vector2(%.5f,%.5f)", t.x, t.y) or tostring(t)
+end
+
+function Vector2.__eq(v1, v2)
+  if (not ffi.istype("vector2", v2)) or (not ffi.istype("vector2", v1)) then return false end
+  return v1.x == v2.x and v1.y == v2.y
+end
+
+function Vector2.__unm(v)
+  return Vector2(-v.x, -v.y)
+end
+
+function Vector2.__div(v1, op)
+  if type(op) == "number" then
+    return Vector2(v1.x / op, v1.y / op)
+  elseif ffi.istype("vector2", op) then
+    return Vector2(v1.x / op.x, v1.y / op.y)
+  else
+    error("Vector2 must be divided by scalar or another Vector2")
+  end
+end
+
+function Vector2.__mul(v1, op)
+  if type(op)  == "number" then
+    return Vector2(v1.x * op, v1.y * op)
+  elseif type(v1) == "number" then
+    return Vector2(op.x * v1, op.y * v1)
+  end
+  return Vector2(v1.x * op.x, v1.y * op.y)
+end
+
+function Vector2.__sub(v1, v2)
+  if type(v1) == "number" then
+    return Vector2(v1 - v2.x, v1 - v2.y)
+  elseif type(v2) == "number" then
+    return Vector2(v1.x - v2, v1.y - v2)
+  end
+  return Vector2(v1.x - v2.x, v1.y - v2.y)
+end
+
+function Vector2.__add(v1, v2)
+  if type(v1) == "number" then
+    return Vector2(v1 + v2.x, v1 + v2.y)
+  elseif type(v2) == "number" then
+    return Vector2(v1.x + v2, v1.y + v2)
+  end
+  return Vector2(v1.x + v2.x, v1.y + v2.y)
+end
+
+function Vector2.split(v)
+  return v.x, v.y
+end
+
+function Vector2.setAngle(v, angle)
+  local magnitude = v.magnitude
+  return Vector2(math.cos(angle) * magnitude, math.sin(angle) * magnitude)
+end
+
+function Vector2.setMagnitude(t, mag)
+  return t.normalized * mag
+end
+
+function Vector2.__newindex(t, k, v)
+  if k == "magnitude" then
+    local result = t:setMagnitude(v)
+    t:set(result)
+  elseif k == "angle" then
+    local result = t:setAngle(v)
+    t:set(result)
+  elseif type(t) == "cdata" then
+    log.error("Cannot assign new property '" .. k .. "' to a Vector2")
+  else
+    rawset(t, k, v)
+  end
+end
+
+function Vector2.getAngle(v)
+  return math.atan2(v.y, v.x)
+end
+
+function Vector2.getNormalized(v)
+  local magnitude = v.magnitude
+  if magnitude == 0 then return Vector2() end
+  return Vector2(v.x / magnitude, v.y / magnitude)
+end
+
+function Vector2.getMagnitude(v)
+  return (v.x^2 + v.y^2)^0.5
+end
+
+function Vector2.__index(t, k)
+  if k == "magnitude" then
+    return Vector2.getMagnitude(t)
+  elseif k == "normalized" then
+    return Vector2.getNormalized(t) 
+  elseif k == "angle" then
+    return Vector2.getAngle(t)
+  end
+  return rawget(Vector2, k)
+end
+
+function Vector2.rotate(t, rad)
+  return Vector2.setAngle(t, t:getAngle() + rad)
+end
+
+function Vector2.set(t, v)
+  if ffi.istype("vector2", v) then
+    t.x = v.x
+    t.y = v.y
+  end
+end
+
+function Vector2.distance(v1, v2)
+  return ((v1.x-v2.x)^2 + (v1.y-v2.y)^2)^0.5
+end
+
+function Vector2.type(v)
+  return "Vector2"
+end
+
+ffi.metatype("vector2", Vector2)
+
+return Vector2

conf.lua

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+function love.conf(t)
+  t.title = "Fractals!"
+  t.window.resizable = true
+
+  t.console = true
+end

gens/circle.lua

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+local circleStack
+local starting_radius = 250
+
+function insertCircle(pos, radius)
+
+  if radius > 2 then
+    table.insert(circleStack, {pos, radius})
+  end
+end
+
+function drawCircle(pos, radius)
+  love.graphics.circle("line", pos.x, pos.y, radius)
+  local offset = Vector2(radius)
+  insertCircle(pos + offset, radius/2)
+  insertCircle(pos - offset, radius/2)
+end
+
+
+return function(offset, scale)
+  circleStack = {}
+  insertCircle(-offset/scale, starting_radius/scale)
+
+  while #circleStack > 0 do
+    local circle = table.remove(circleStack)
+    drawCircle(unpack(circle))
+  end
+end

gens/triangle.lua

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+local originalSize = 1000
+local halfSqrt3 = 0.5*3^0.5
+local trianglesToDraw = {}
+
+local function insertTriangle(pos, size, triangleType)
+  pos = pos or Vector2()
+  size = size or originalSize
+
+  local visibleSize = Vector2(love.graphics.getDimensions())+size
+ 
+  local modifiedPosition = pos + size/2 
+
+  if (modifiedPosition.x > 0 and modifiedPosition.x < visibleSize.x and modifiedPosition.y > 0 and modifiedPosition.y < visibleSize.y) then
+    table.insert(trianglesToDraw, {
+      pos = pos,   size = size,
+      triangleType = triangleType or "full"
+    })
+  end
+end
+
+local function drawTriangle(pos, size, triangleType)
+  if size <= 6.5 then return end
+  local h = size * halfSqrt3
+  local halfSize = size/2
+  local halfH = h/2
+
+  if triangleType == "full" then
+    love.graphics.line(pos.x, pos.y-halfH, pos.x+halfSize, pos.y+halfH, pos.x-halfSize, pos.y+halfH, pos.x, pos.y-halfH)
+  elseif triangleType == "top" then
+    love.graphics.line(pos.x+halfSize, pos.y+halfH, pos.x-halfSize, pos.y+halfH)
+  elseif triangleType == "left" then
+    love.graphics.line(pos.x, pos.y-halfH, pos.x+halfSize, pos.y+halfH)
+  elseif triangleType == "right" then
+    love.graphics.line(pos.x-halfSize, pos.y+halfH, pos.x, pos.y-halfH)
+  end
+
+  insertTriangle(pos + Vector2( 0     , -h/4), halfSize, "top")
+  insertTriangle(pos + Vector2( size/4,  h/4), halfSize, "right")
+  insertTriangle(pos + Vector2(-size/4,  h/4), halfSize, "left")
+end
+
+return function(offset, scale)
+  trianglesToDraw = {}
+  insertTriangle(-offset/scale, originalSize/scale)
+
+  while #trianglesToDraw > 0 do
+    local triangle = table.remove(trianglesToDraw)
+    drawTriangle(triangle.pos, triangle.size, triangle.triangleType)
+  end
+end

main.lua

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+Vector2 = require("Vector2")
+local showDebug = false
+
+local generator = require("gens.circle")
+local scaleSpeed = 0.1
+
+love.graphics.setNewFont(25)
+
+local function resetCamera()
+  scale = 1
+  offset = -Vector2(love.graphics.getDimensions())/2
+end
+
+
+resetCamera()
+
+function round(num, numDecimalPlaces)
+  local mult = 10^(numDecimalPlaces or 0)
+  return math.floor(num * mult + 0.5) / mult
+end
+
+function math.clamp(x, min, max)
+  return (x < min and min) or (x > max and max) or x
+end
+
+
+function love.keypressed(keycode, scancode)
+  if scancode == "space" and love.keyboard.isDown("lctrl") then
+    love.window.setFullscreen(not love.window.getFullscreen())
+  elseif scancode == "f1" then
+    showDebug = not showDebug
+  elseif scancode == "f2" then
+    resetCamera()
+  end
+end
+
+function love.mousemoved(x, y, dx, dy)
+  if love.mouse.isDown(1) then
+    offset = offset - Vector2(dx, dy)*scale
+  end
+end
+
+function love.wheelmoved(x, y)
+  if y == 0 then return end
+  local oldScale = scale
+  if y < 0 then
+    scale = scale*(1+scaleSpeed)
+  else
+    scale = scale*(1-scaleSpeed)
+  end
+  offset = offset + Vector2(love.mouse.getPosition()) * (oldScale-scale)
+end
+
+
+function love.draw()
+  love.graphics.setColor(1, 1, 1, 1)
+  generator(offset, scale)
+
+  if showDebug then
+    love.graphics.setColor(0.8, 0.2, 0.2)
+    love.graphics.print("Offset: ("..round(offset.x, 2)..";"..round(offset.y, 2)..")", 0, 0)
+    love.graphics.print("Zoom: "..(1/scale), 0, 30)
+  end
+end