Type: Mandelbrot set Algorithm: Color (Accurate) Real: -1.786440646916 ... -1.786439646916 Imaginary: -0.000000500000 ... +0.000000500000 Iteration: 3000 Pixels: 400 x 400 Type: Mandelbrot set Algorithm: Color (Boundary) Real: -0.108203652781 ... -0.107574830106 Imaginary: +0.649247769604 ... +0.649876592279 Iteration: 10000 Pixels: 400 x 400 Type: Mandelbrot set Algorithm: Color (Boundary) Real: -0.811496603038 ... -0.811494391108 Imaginary: -0.201326453221 ... +0.201324241291 Iteration: 5000 Pixels: 400 x 400 Type: Mandelbrot set Algorithm: Color (Accurate) Real: -1.117152521437 ... -1.117141870342 Imaginary: +0.222211410390 ... +0.222222061485 Iteration: 5000 Pixels: 400 x 400 Type: Mandelbrot set Algorithm: Color (Boundary) Real: -0.613510378964 ... -0.613510378924 Imaginary: -0.677576600968 ... -0.677576600928 Iteration: 5000 Pixels: 400 x 400 Type: Julia set Algorithm: Color (Boundary) c = -0.125475000000 + 0.749400000000 i Real: -1.400000000000 ... +1.400000000000 Imaginary: -1.400000000000 ... +1.400000000000 Iteration: 100 Pixels: 400 x 400 Type: Mandelbrot set Algorithm: Color (Fast) Real: -0.173538390000 ... -0.144828555000 Imaginary: +1.018767645000 ... +1.047477480000 Iteration: 200 Pixels: 400 x 400 Type: Julia set Algorithm: Color (Boundary) c = -0.157414272428 + 1.033054947853 i Real: -1.400000000000 ... +1.400000000000 Imaginary: -1.400000000000 ... +1.400000000000 Iteration: 100 Pixels: 400 x 400 Type: Julia set Algorithm: Color (Boundary) c = -0.810000061989 - 0.344999969006 i Real: -1.700000000000 ... +1.700000000000 Imaginary: -1.700000000000 ... +1.700000000000 Iteration: 5000 Pixels: 400 x 400 Type: Julia set Algorithm: Color (Boundary) c = -0.764312625000 + 0.132699750000 i Real: -1.600000000000 ... +1.600000000000 Imaginary: -1.600000000000 ... +1.600000000000 Iteration: 500 Pixels: 400 x 400 Type: Julia set Algorithm: Color (Accurate) c = -0.747593803839 + 0.083586811697 i Real: -1.600000000000 ... +1.600000000000 Imaginary: -1.600000000000 ... +1.600000000000 Iteration: 5000 Pixels: 400 x 400 Type: Julia set Algorithm: Color (Accurate) c = -1.401154945839 + 0.000000000000 i Real: -2.000000000000 ... +2.000000000000 Imaginary: -2.000000000000 ... +2.000000000000 Iteration: 500 Pixels: 400 x 400 Type: Mandelbrot set Algorithm: Color (Boundary) Real: -0.747733627331 ... -0.747487242322 Imaginary: +0.083463619193 ... +0.083710004202 Iteration: 5000 Pixels: 400 x 400 Type: Mandelbrot set Algorithm: Color (Boundary) Real: -0.748778345558 ... -0.740295245933 Imaginary: +0.120546650207 ... +0.129029749832 Iteration: 5000 Pixels: 400 x 400 Type: Mandelbrot set Algorithm: Color (Boundary) Real: -0.748689541691 ... -0.748687541691 Imaginary: +0.084371659093 ... +0.084373659093 Iteration: 5000 Pixels: 400 x 400 Type: Mandelbrot set Algorithm: Color (Boundary) Real: -0.748828272213 ... -0.748558043493 Imaginary: +0.084322618670 ... +0.084592847389 Iteration: 5000 Pixels: 400 x 400 Type: Mandelbrot set Algorithm: Color (Boundary) Real: +0.250186793448 ... +0.250186864544 Imaginary: -0.000003799402 ... +0.000003728306 Iteration: 3000 Pixels: 400 x 400 Type: Mandelbrot set Algorithm: Color (Boundary) Real: +0.250187685606 ... +0.250188625606 Imaginary: -0.000004553197 ... -0.000003613197 Iteration: 3000 Pixels: 400 x 400 Type: Mandelbrot set Algorithm: Color (Boundary) Real: +0.250184360754 ... +0.250188854379 Imaginary: -0.000005502842 ... -0.000001009218 Iteration: 30000 Pixels: 400 x 400 Type: Mandelbrot set Algorithm: Color (Boundary) Real: +0.250354264973 ... +0.250354868999 Imaginary: -0.000010863155 ... -0.000010259129 Iteration: 25000 Pixels: 400 x 400 Type: Mandelbrot set Algorithm: Color (Boundary) Real: +0.250186507682 ... +0.250187298560 Imaginary: -0.000005138284 ... -0.000004347406 Iteration: 30000 Pixels: 400 x 400 Type: Mandelbrot set Algorithm: Color (Boundary) Real: +0.250354462190 ... +0.250354464307 Imaginary: -0.000010700562 ... -0.000010698446 Iteration: 25000 Pixels: 400 x 400 Type: Julia set Algorithm: Color (Accurate) c = +0.250165658404 - 0.000003772500 i Real: -1.500000000000 ... +1.500000000000 Imaginary: -1.500000000000 ... +1.500000000000 Iteration: 30000 Pixels: 400 x 400 Type: Julia set Algorithm: Color (Accurate) c = +0.250167065178 - 0.000004058623 i Real: -1.500000000000 ... +1.500000000000 Imaginary: -1.500000000000 ... +1.500000000000 Iteration: 30000 Pixels: 400 x 400 Type: Julia set Algorithm: Color (Accurate) c = +0.250166445243 - 0.000003700969 i Real: -1.500000000000 ... +1.500000000000 Imaginary: -1.500000000000 ... +1.500000000000 Iteration: 30000 Pixels: 400 x 400 マンデルブロート集合とさまざまなジュリア集合以下にマンデルブロート集合とその一部分の拡大、それにいろいろなパラメータに対応するジュリア集合の図を示しました。 ( 数学的な背景については別のポスターで説明していますので、そちらを参照してください。) マンデルブロート集合の全体図に小さな赤い点で示してあるものは、その点を中心とするマンデルブロート集合の拡大図です。拡大率はそれぞれの図で全然違いますので注意してください。青い点で示してあるものがその点をパラメータとするジュリア集合です。右下や左上のジュリア集合の図を見ると、パラメータのごくわずかな変化でジュリア集合に大きな変化が起きる場合があることがわかります。このような部分でどれ程複雑な現象が起きているかについてはまだ完全には解明されていません。

マンデルブロート集合とさまざまなジュリア集合inou/opencampus/...Type: Mandelbrot set Algorithm: Color (Accurate) Real: -1.786440646916 ... -1.786439646916 Imaginary:

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Page 1: マンデルブロート集合とさまざまなジュリア集合inou/opencampus/...Type: Mandelbrot set Algorithm: Color (Accurate) Real: -1.786440646916 ... -1.786439646916 Imaginary:

Type: Mandelbrot setAlgorithm: Color (Accurate)Real: -1.786440646916 ... -1.786439646916Imaginary: -0.000000500000 ... +0.000000500000Iteration: 3000Pixels: 400 x 400

Type: Mandelbrot setAlgorithm: Color (Boundary)Real: -0.108203652781 ... -0.107574830106Imaginary: +0.649247769604 ... +0.649876592279Iteration: 10000Pixels: 400 x 400

Type: Mandelbrot setAlgorithm: Color (Boundary)Real: -0.811496603038 ... -0.811494391108Imaginary: -0.201326453221 ... +0.201324241291Iteration: 5000Pixels: 400 x 400

Type: Mandelbrot setAlgorithm: Color (Accurate)Real: -1.117152521437 ... -1.117141870342Imaginary: +0.222211410390 ... +0.222222061485Iteration: 5000Pixels: 400 x 400

Type: Mandelbrot setAlgorithm: Color (Boundary)Real: -0.613510378964 ... -0.613510378924Imaginary: -0.677576600968 ... -0.677576600928Iteration: 5000Pixels: 400 x 400

Type: Julia setAlgorithm: Color (Boundary)c = -0.125475000000 + 0.749400000000 iReal: -1.400000000000 ... +1.400000000000Imaginary: -1.400000000000 ... +1.400000000000Iteration: 100Pixels: 400 x 400

Type: Mandelbrot setAlgorithm: Color (Fast)Real: -0.173538390000 ... -0.144828555000Imaginary: +1.018767645000 ... +1.047477480000Iteration: 200Pixels: 400 x 400

Type: Julia setAlgorithm: Color (Boundary)c = -0.157414272428 + 1.033054947853 iReal: -1.400000000000 ... +1.400000000000Imaginary: -1.400000000000 ... +1.400000000000Iteration: 100Pixels: 400 x 400

Type: Julia setAlgorithm: Color (Boundary)c = -0.810000061989 - 0.344999969006 iReal: -1.700000000000 ... +1.700000000000Imaginary: -1.700000000000 ... +1.700000000000Iteration: 5000Pixels: 400 x 400

Type: Julia setAlgorithm: Color (Boundary)c = -0.764312625000 + 0.132699750000 iReal: -1.600000000000 ... +1.600000000000Imaginary: -1.600000000000 ... +1.600000000000Iteration: 500Pixels: 400 x 400

Type: Julia setAlgorithm: Color (Accurate)c = -0.747593803839 + 0.083586811697 iReal: -1.600000000000 ... +1.600000000000Imaginary: -1.600000000000 ... +1.600000000000Iteration: 5000Pixels: 400 x 400

Type: Julia setAlgorithm: Color (Accurate)c = -1.401154945839 + 0.000000000000 iReal: -2.000000000000 ... +2.000000000000Imaginary: -2.000000000000 ... +2.000000000000Iteration: 500Pixels: 400 x 400

Type: Mandelbrot setAlgorithm: Color (Boundary)Real: -0.747733627331 ... -0.747487242322Imaginary: +0.083463619193 ... +0.083710004202Iteration: 5000Pixels: 400 x 400

Type: Mandelbrot setAlgorithm: Color (Boundary)Real: -0.748778345558 ... -0.740295245933Imaginary: +0.120546650207 ... +0.129029749832Iteration: 5000Pixels: 400 x 400

Type: Mandelbrot setAlgorithm: Color (Boundary)Real: -0.748689541691 ... -0.748687541691Imaginary: +0.084371659093 ... +0.084373659093Iteration: 5000Pixels: 400 x 400

Type: Mandelbrot setAlgorithm: Color (Boundary)Real: -0.748828272213 ... -0.748558043493Imaginary: +0.084322618670 ... +0.084592847389Iteration: 5000Pixels: 400 x 400

Type: Mandelbrot setAlgorithm: Color (Boundary)Real: +0.250186793448 ... +0.250186864544Imaginary: -0.000003799402 ... +0.000003728306Iteration: 3000Pixels: 400 x 400

Type: Mandelbrot setAlgorithm: Color (Boundary)Real: +0.250187685606 ... +0.250188625606Imaginary: -0.000004553197 ... -0.000003613197Iteration: 3000Pixels: 400 x 400

Type: Mandelbrot setAlgorithm: Color (Boundary)Real: +0.250184360754 ... +0.250188854379Imaginary: -0.000005502842 ... -0.000001009218Iteration: 30000Pixels: 400 x 400

Type: Mandelbrot setAlgorithm: Color (Boundary)Real: +0.250354264973 ... +0.250354868999Imaginary: -0.000010863155 ... -0.000010259129Iteration: 25000Pixels: 400 x 400

Type: Mandelbrot setAlgorithm: Color (Boundary)Real: +0.250186507682 ... +0.250187298560Imaginary: -0.000005138284 ... -0.000004347406Iteration: 30000Pixels: 400 x 400

Type: Mandelbrot setAlgorithm: Color (Boundary)Real: +0.250354462190 ... +0.250354464307Imaginary: -0.000010700562 ... -0.000010698446Iteration: 25000Pixels: 400 x 400

Type: Julia setAlgorithm: Color (Accurate)c = +0.250165658404 - 0.000003772500 iReal: -1.500000000000 ... +1.500000000000Imaginary: -1.500000000000 ... +1.500000000000Iteration: 30000Pixels: 400 x 400

Type: Julia setAlgorithm: Color (Accurate)c = +0.250167065178 - 0.000004058623 iReal: -1.500000000000 ... +1.500000000000Imaginary: -1.500000000000 ... +1.500000000000Iteration: 30000Pixels: 400 x 400

Type: Julia setAlgorithm: Color (Accurate)c = +0.250166445243 - 0.000003700969 iReal: -1.500000000000 ... +1.500000000000Imaginary: -1.500000000000 ... +1.500000000000Iteration: 30000Pixels: 400 x 400

マンデルブロート集合とさまざまなジュリア集合以下にマンデルブロート集合とその一部分の拡大、それにいろいろなパラメータに対応するジュリア集合の図を示しました。( 数学的な背景については別のポスターで説明していますので、そちらを参照してください。)マンデルブロート集合の全体図に小さな赤い点で示してあるものは、その点を中心とするマンデルブロート集合の拡大図です。拡大率はそれぞれの図で全然違いますので注意してください。青い点で示してあるものがその点をパラメータとするジュリア集合です。

右下や左上のジュリア集合の図を見ると、パラメータのごくわずかな変化でジュリア集合に大きな変化が起きる場合があることがわかります。このような部分でどれ程複雑な現象が起きているかについてはまだ完全には解明されていません。