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.

Impulse

x ↦ 0.7280723536001950y² - 0.4285976376157210xy - 0.00504638252707146000y - 2.10138726728836x² - 1.20138428551700x + 0.1084001644604770


y ↦ -2.67993708147439y² + 0.6196384648658460xy - 0.5113698046489240y - 0.3187101296250590x² - 0.1522131699603020x + 0.3688420719297350

Starting point (0,1;0,5); 50000 iterations; first 200 are not drawn. Click to get 300 dpi version.

Dolphin plays

Red component corresponds to partial derivative by x, blue corresponds to partial derivative by y, green depends on them in a some strange illogical way and added to make picture more lovely.

x ↦ 0.3663914416345010y² - 1.03747828322561xy -
1.50178812723409y + 1.16992005362711x² + 1.99643560701994x +
0.3626745632492520

y ↦ -1.02282315224122y² + 1.76994066384234xy +
0.3215114959922850y - 0.4038307575891870x² - 0.1628996674407880x +
1.49434629375527

Starting point (0,1;0,5); 50000 iterations; first 200 are not drawn. Click to get 300 dpi version.

The March Hare

x ↦ -0.4814599171946820y² + 1.04099727230385xy +
0.7395358611379820y - 1.24737384814668x² - 1.96139561496028x -
0.3909564561259940

y ↦ -0.7294262704650580y² + 0.4968559173666280xy +
1.52447124466781y + 2.76842854599995x² - 2.47576632778457x -
0.7309209969132820

Starting point (0,1;0,5); 50000 iterations; first 200 are not drawn. Click to get 300 dpi version.

Feeling of Escher

This image is full of artistic expression.

x ↦ 0.650850850949240y² - 1.64884940553219xy -
0.6016011453529680y - 0.3473171828135250x² + 1.66145047715947x +
0.026518324295271800

y ↦ 0.414088889877770y² - 2.68030523991092xy +
0.1142930556175630y - 2.48282952418330x² + 1.48569354388800x +
0.8157087840835780

Starting point (0,1;0,5); 50000 iterations; first 200 are not drawn. Click to get 300 dpi version.

Möbius nightmare

Not really Möbius but looks pretty nice anyway.

x ↦ -0.104776680215230y² + 1.54876597480441xy +
0.043730911135073200y - 1.12780069118847x² - 1.63073613988159x +
0.4474983408487380

y ↦ -2.12534488089094y² - 1.85727434131060xy +
1.41227652801728y + 2.73903100990934x² + 0.597063987152260x +
0.2924226813599350

Starting point (0,1;0,5); 50000 iterations; first 200 are not drawn. Click to get 300 dpi version.

Paper

x ↦ 1.40936648408379 - 1.26965791645760x - 2.09733184273639y - 1.44917724644668xy - 1.49373403181735x² -0.397197354833836y²

y ↦ -0.444398110064565 - 0.527210197459999x + 1.57942039911374y + 2.51450650465324xy - 1.03619730603340x² + 0.478557808944680y²

Starting point (0,1;0,5); 50000 iterations; first 200 are not drawn. Click to get 300 dpi version.