Black hole

x ↦ -0.9208898452045490y² + 0.8952066957450720xy + 1.29690105688198y - 0.6718008096375430x² - 1.27506260389526x - 0.3306488696530980

y ↦ -2.83239225043423y² + 1.63633718261426xy + 2.58028867963036y - 2.60270176665395x² - 1.93174765601573x + 0.2812448271223420

Starting point (0,1;0,5); 50000 iterations; all are drawn. Color version has point thickness increased. Click pictures to get 300 dpi versions — you want to do it.

You may want to see what's inside the central “black hole”, so here comes magnified version of the core. Click to see 300 dpi version.