A instance variable in ruby has a name beginning with @. It often makes sense for it to be initialised at setup (not necessarily in the loop could be set in a called method).

def setup
  sketch_title 'Tree'
  color_mode RGB, 1
  frame_rate 30
  @x = 0.0
  @dx = width / 100
  @start_time = Time.now
  @frame_time = nil
end

def draw
  ...
  @x += @dx
  if @x < 0
    puts "Time after this iteration: " + (Time.now - @start_time).to_s
  end
  ...
end

For a variable that gets called quite a lot in a JRubyArt sketch it makes sense to create a getter using attr_reader. This has the fortunate side effect of making it blindingly obvious when you are assigning it to a new value/instance (it also makes the sketch variable read only visible externally, PS: if this concerns you don’t use ruby).

attr_reader :x, :y

def setup
  sketch_title 'Interpolate'
  @x, @y = 0, 0
  no_stroke
end

def draw
  background(51)
  @x = lerp(x, mouse_x, 0.05)
  @y = lerp(y, mouse_y, 0.05)
  fill(255)
  stroke(255)
  ellipse(x, y, 66, 66)
end

def settings
  size(640, 360)
end