This is a super hacky program to generate a picture that I hope will resemble the one here: http://felifee.deviantart.com/art/fire-blossom-364662404. I'm not too familiar with Maxima, so I'm just slapping stuff together until I better understand how the "language" works until I attempt to refactor this code.

fire_blossom.wxm

load(draw);

draw_polar(expr,range) :=
    block([theta_var: range[1]],
      draw2d(background_color = black,
             xtics = 'none,
             ytics = 'none,
             axis_top = false,
             axis_bottom = false,
             axis_left = false,
             axis_right = false,
             xrange = [-3,3],
             yrange = [-3,3],
             nticks = 1000,
             dimensions = [1000,1000],
             terminal = png,
             file_name = "fire-blossom",
             line_width = 10,
             color = "#95A161",
             parametric(cos(theta_var)*(expr), sin(theta_var)*(expr), theta_var,range[2],range[3]),
             color = "#DCFBCF",
             parametric(cos(theta_var)*(expr-0.2), sin(theta_var)*(expr-0.2), theta_var,range[2],range[3]),
             color = "#D3AF10",
             parametric(cos(theta_var)*(expr-0.4), sin(theta_var)*(expr-0.4), theta_var,range[2],range[3]),
             color = "#8A0F00",
             parametric(cos(theta_var)*(expr-0.6), sin(theta_var)*(expr-0.6), theta_var,range[2],range[3]),
             color = "#801004",
             parametric(cos(theta_var)*(expr-0.8), sin(theta_var)*(expr-0.8), theta_var,range[2],range[3]),
             color = "#260000",
             parametric(cos(theta_var)*(expr-1), sin(theta_var)*(expr-1), theta_var,range[2],range[3]),
             color = "#95A161",
             parametric(cos(theta_var)*(expr-1.2), sin(theta_var)*(expr-1.2), theta_var,range[2],range[3]),
             color = "#DCFBCF",
             parametric(cos(theta_var)*(expr-1.4), sin(theta_var)*(expr-1.4), theta_var,range[2],range[3]),
             color = "#D3AF10",
             parametric(cos(theta_var)*(expr-1.6), sin(theta_var)*(expr-1.6), theta_var,range[2],range[3]),
             color = "#8A0F00",
             parametric(cos(theta_var)*(expr-1.8), sin(theta_var)*(expr-1.8), theta_var,range[2],range[3]),
             color = "#801004",
             parametric(cos(theta_var)*(expr-2), sin(theta_var)*(expr-2), theta_var,range[2],range[3]),
             color = "#260000",
             parametric(cos(theta_var)*(expr-2.2), sin(theta_var)*(expr-2.2), theta_var,range[2],range[3])
));

draw_polar(3 + sin(5*t)/2 + sin(50*t)/5, [t,0,2*%pi]);