My first somewhat complex sketch using the ruby-processing library, https://github.com/jashkenas/ruby-processing. The output is here: http://quephird.deviantart.com/art/fire-blossom-clone-draft-2-366332642

fire_blossom.rb

require 'rubygems'
require 'ruby-processing'

class FireBlossom < Processing::App
  @@width = 1980
  @@height = 1024
  @@blossom_colors = [[63,7,0],[102,35,9],[142,20,0],[197,70,3],[189,125,1],[223,222,106],[190,237,229],[132,139,62]]

  def setup
    size @@width,@@height
    background 0
    no_loop
  end

  def f (r, t)
    r + r*sin(5.0*t)/10.0 + r*sin(50.0*t)/10
  end

  def blossom_ring_segment (r, t, dt)
    f1 = f(r,t)
    x1 = f1*cos(t)
    y1 = f1*sin(t)
    f2 = f(r,t+dt)
    x2 = f2*cos(t+dt)
    y2 = f2*sin(t+dt)
    line x1,y1,x2,y2
  end

  def blossom_ring (r, c)
    stroke *c
    dt = Math::PI/360
    (0..2*Math::PI).step(dt).each {|t| blossom_ring_segment r, t, dt}
  end

  def draw
    translate @@width/2,@@height/2
    stroke_width 2
    (0..1000).each {|r| blossom_ring r, @@blossom_colors[(r/30)%@@blossom_colors.length]}
    save "fire_blossom.png"
  end
end

FireBlossom.new :title => "fire blossom"