Logiciel libre de géométrie, d'analyse et de simulation multiplateforme par Yves Biton

# Example of a complex recurrent sequence graph : The set of Mandelbrot

modification lundi 31 août 2019.

Toutes les versions de cet article : [English] [Español] [français]

In this example we will illustrate the set of Mandelbrot which is the set of the points with complex affix z such as the complex recurrent sequence $z_n$ defined by $z_0=0$ et $z_{n+1}={z_n}^2+c$ is bounded (which is true if it is convergent).

For a more agreable figure, I suggest that you start from a figure with a background image and a frame convenient to to this image.

In MathGraph32 (JavaScript version), utilisez l’icône and ask for new figure by Base 64 code.

In the dialog box asking for the Base 64 code, enter the code below :

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Ad+4H+NF5dpFrVrZtqdvPFcNIrIUBKbf759icCvUnnXJGLgjjp5bOTkm9jxh7YqenaiO3OR2ruvE+l2EM0UdlB5TID5oHIJ9c1hW+nSyyBYo2Y+gHNe5SrqcFNI8+futxOh8KaPY#YTelHmuoyT5YYLsPbHrmp#F7w6SbHVdUntluw6uLdSyrHCfvHP8TZpuj6dPa3MRnjdI9wznIz9feuP+K+s63baPBpd8sLrLI0glAG5UJ4XHbpXzOa01Oom5Np#gexllTR2ST#E9Blu9Hm0C1uLeWeGO#kMUa3DmTa3bPpu61DpugOJ5PljEsfzBplJQAdc4rxP4d6nfHxVZWzXf+jF8sZzujiA#jIPoOPxr0nxR8WNO0zxRbzaVcvPawl457ZeVbjhvcH61lSxEqdN0ujNa2FVSpGp1XcbL4j0nT#HTK+ryTrcQBvNhOY2bONirn8MGui8ayp4e8PXd#b3RiG1fNjijDSqW5G7+7Xz#AOINfg1XXl1az02OxlyHZEbKFh3A7fSqmo+ItY1W4uJ77UJ5XuMebluHx0yKxgpQjyxbsdE4xlJSa2PcNW8bWFn4J0y+tdQVryVUE6HaZlGfvVBffGTTLDULpbGQXFutun2YiL7z#wAW73614FnPU0Zp+9bdi5Ifyo92k#aEjkjeGTQormA8CNxgY#WvO#EnibwzrrvNB4WFhcMc77e4KqfquMVxuTSZqXBN8xSdlYlmMJYGFWUf7RzT4WtVKGaN3H8QVsZ+lV6M1e4j0vw38Q#DfhjY9l4Mge4X#l4nmMj#AF5GBXWy#tArcwSK+mCJtnycZ5yOPpXhAJx1oJPrUxilqhytJWaPfU+K+j3g1xnu2iRYA9kvlfMZMDIX2z61em8Vacvw9fVW1FEvpFXetugMkYPTPPBNfOlKJGClQxAPUA8GqfN3IUIdj6h0O2j1fQbPVnmEsRg3qpTbM4X7xx3+orMGvWeqeMrODT9cl3wQGZmYhIh6K#p6GvE9I8c+INHvYLmC#dzBEYY1l5VUPVR6VJ4W1XR7DxI2qazBcS2+5n+zwnhyecMf7tTUlKUVFvYdOnGMnJLc9o17RVjuQ4jRJJDvdUfcoJ9D3q#4asrjT9RFukyLPOnMG752Hrj+tUtI8b6P4l8SzIJ4LbSYookjDjkyMBhU7nFcx8UfFmo+GvFP2LTljtbuOPa80YzviPI565rvqY+ToqlHX1OCngf3znLRdLHo9zeh7i107Q9SlmubqRsrIm#ytnLszdQD0qh4u0y91yzAtCypApe4ik+UK2Om31968q+G3iK0n8cTXevTyiS5XdujkKqxAztwOufSvS9e1u6ns#MhkdI7yPcykYZRnpXNl1OUcTeL1N8e4qik1p+p5XPDzkAYPQ1WaHmtq5gO88flVQwc9K+zv3PGjPsZwi9qPJPpXT6FpVrfanFbXjTJFIdgaEAnNdZJ8NCNaSFJWbTy+xpejA4#lWFXF0qc+Wb1sXFyl8J5cITnpVmGHOeD#ntXR6n4VvdLjaeWLbbmVo42bq2O9UYrUhhx0NawqRnHmg9CJTadpHdeG7M6DpD3UZfUJbgpE9tZqGkiLH7#AD2UYzXF+LoEtNVuLeG7e6XJ3yHjcc9Peu28EafJJeNP5kkUUI5KHlyf4awPGNvcaj4jnQQKJVPlhIxxn2rz6DtipJu6sVdcidup5rMnbFVHUCuvs#D0t7feQ6SRqoLSMVPyqOprmbyIRzOi5IBOCR1FejdPRG9OpfQoMOaawqRhzUbZqWdCGUw0+mmpZoNNe6#s4#8AMzf9uv8A7Vrws17p+zj#AMzN#wBuv#tWuDMP93l8vzRdP4jwY#eP1opT94#WkrYAooopgFFFFABS4oxS0wE6UUHrRQAUUUUxBS4pKWmAUUUUAFLiiimAUUUUCCiilpgFL1pMUtFhCYopaKYBRRS4pgJS4paWiwhuKUClxS4ppAJiilpcUwuNopwFLigVxtFOxRigLiYpaWiiwhKOtLilxTFcTFKBSgUooC4AUClApQKYgApwHNGKUU0S2L3qRRmmqvNSgdqZLY5RViIVCo6VZjHNMykzc0rVbvT5o5bed0ZCWUZ4BPBOK2rS#nmIQu7bmyFBJ5rloeCK6zwpBdT6vB9ljLvGwdjtyFHrWFVQhGU5LY5px5pWO78OgyQvbSyy27yOG85Thkx1x715F8XPDE+l60dSuNRjmW4#1aPJukK9icevWvbbrXbHTJr9r4KiIn7vzRsEzkchSP4cfrXzZ441az1fX2m0+SZrJRiJJSSYz3UZ7elfGVKsa9b2lNdNT6DD0pUqXLLboRz+Odektre1S8eO3tgoiRT93HQ#Wtbwr48e08aQ63rm66IIDHoox3I71wp4PNA70nCNrG3Mz6jtmfxDpUuol98M0zSWyyKFlER6ZX0z0NTW2jXIsLhbZgly6EA5wwHdh3GK5#4UXUNt4CuNb1NkAXFvHLOSCxU8Jn+70+lcb4l+J0dvr41Lw8skNwyPHcxu26MN03Ia3WIkqHsU9zkeGUq#tTpvC3jvSrS7vtOvrpxLZwyKl3O5MYx0wvXOfWuV8T#FlNd0ddMudHtL6RVKNczLzuBOGUjtivN9Q1K61W8e6vJfMmk+8QAM#gKqZrFLSzOptN8xI1y+ZAmI1f7ypwKjDY6U2imIcWPSkzmkooAKXNJRQAuaTNFFABmjNFFABmjNFFAC5ozikooAXdS7+MYptFFwHpK8bh0YqwOQVOCK0dS1u91iO3GoSmeWBPLSZuX29gT3xWXSg0Aev#CrTfCkV7FeT+IHGpHAS28gDb1PJPXpXpBgtvEcEuo2h3xB2jRHYIXf+6p6fSvltHaMhkYhuxBwRXTJ471geEx4d87bAkyyQyDho8dRWlKpOk249TOrRhVSUtkexX1lpuoi5t7FHjutOUecpXhs#wC10zXMGyO#AznPTHSuq8K3GmWHw#ikuNYtbuRSEka3+8A3OCT94#yqRNLWcQzW+WhmG6MsMEivXy3GScHGpI8rHUFCadNOxR0vw1fEC4IW3UEYaRtrEnpge9dXNrdl4dn03StTvBCbolpmlJ4A6KB1yTWF4y8WyeFdKtrmK4gbULK4CfZbkDdKjAfMB1wO2a8V8TeONU8UanBe3QjVrZy0GBynOcZ7815mLxdXEtwdrHfhsJCklN7tH0b4i0u61NYHBzEM+Sj8My+uKrHwVp8kMZiaSOaSMuqcHJX72K8Q0D4q+ItL16PUbu6a9BURSCXk+XnJC+hqfW#ijr154tlvtKu3gty5FvEF4Abg8etSsZiIRUI6fkDwNKUm3qe4aJoNxpl3DPIyL#EEL4Yj1x#Wn64thojPfjT#ALVO8m5ZWPyo3t60tibmPw1a3iype6kYMS3cvDkEcrjtjp+FY2i+KoxcGwvpI#szlirTDIVveurDutiP3ztbsjjrxpUH7Jb9zk9Z8dak7MIY4bfLHIROeeoNec3cjSyu7nLE5JPeu88WaHZ6ZbG6a#Wd7hi0SRDIIJ7nsa8#m5+tfRUVDkTijCktSq3WozzxUj0w1ozsRGaaacR1ppqGWhpr3T9nL#mZf+3X#wBq14ZXun7OX#My#wDbr#7VrhzD#d5fL80aU#iR4M33j9aSlb7x+tJWwBRRRQAUYpRS0wEooooAKKKKYgoxRS0wCiiigAxS0UUxBRRRQAUtFFMAoxRiloEFFFFUAtApQKUCgQgFLil20uKoTYmKMU7FGKBXExRinUYosFxMUYpcUoFFhXEwaMGlxRimAlGKdijj1oATFLilopgJS0uKNpoEFApcUoFFhNgKUUAU7jtTsJsQU8ChR7VIq0yRVHFPUZoVeelTImaNiGwRfarKL7U6KEngA1eWxlRtjxurjkqy4NDaTszGUrkUKnPSug0W#utOlL2kzxMww204yKzI7cg4rRtYDuFRNxlF3MJSdz0eDWbLVYBay2YuYyu#ypRyzgdj2zivJfiR4ba+kXWNH0eW1s44h5yPhdrd1UfxfUV3mm2dzA6Pscc8Y611Lf2XNZi51oxTw2bbM7#9UX#TnrXy+MwlODU6ctPzPVweLm7xqRu#yPklgQSCMEdQaVFG4biVU9T7V6#4913wLpVxJZ6T4dhvL9RsM87Havo2B1z1ryK4uJLmUvIRnsFGAPpXCpX3R6TVjc1jxZe6nplnpKMYNMs02RQIcBj3ZvUmufyMUhpKaVthPUXiikooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigApaSigBc0oIFNooAv6dqUmn3kEyqsqRSLL5MnKMw9RX0L8PPHtn4uvfs2p3CJqEr5itwoVIlHRVPfNfNgOKmtrqa0uY7i3kaKaNgyOpwVI9KE7O6FOPOuVnbfFm7lk8cXVnISRaExgty2M5+91PWuEzXQ+KvEJ8VXcWrXEapfmJYrkqOJGAwH+pHWudxzSjtYpj8jH9a9F+D19p6eJmsdT0+O7huFzHmIu8bjuuO9ec4O32r0f4Y6f4n0++TXtHshLAX8idio3LGepXPrzzSn8LHH4j1rxXqN9JHJYxJiFR82xfmI7A4#WvML6VlPPI#zwK90YqLdrgWqQF4yFS4cbnY9ifcYrxLxVqx1LUOLWK0SBfKWGI5AIPJz3NfRZXVjKPLGFkjwcRSkppyd7nO3VzJJ952bHTJrOk5NWZj+dVXPIr2C4aEDVGalbpURqWboYaaafTDUstMaa90#Zy#5mX#t1#8AateGGvdP2cv+Zl#7df8A2rXBmH+7y+X5o1p#EjwVvvH60lK33j9aStgCilopgLRSUUwCiiigQUClFFMAooooAKWiimIKKKWgBKWigUwCgUUtMQUYpaAKYBigUopRQACngUgFPAqkiGxMUoWnKuakWP2qrEtkW2jFTeWR2o207CuQ4oxUpWk20WHcZ+FH4U#FAApAMxS4p+BRigVxuKNtOxRtNAXExS4FLto20wuNIpQKdtpQKBXGYpQKdilC0xXGgU8LQFqTFAmxAKkV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UupFHFY+GdIFvYyNFHMEkW2H3YjtG4A#WrlrqM97pF2fNZAVKqUIGTXGeJtUvft7wXgMZQkqhAyAfp2rPtfENxbWdxaoymObAbPb6V7tPLubD269Tx54x+25+h1Ph#R9N0K3vbVpbe7fUBiZoo9uVPPX05qv8S1k0r4fSW+jW0FrGUCFoz+9A7Ljqc+tYumaq1vcxzgbipztJ4Psa7LTvI1+7jlurBJnhcOjgkbD2B9RXFjMudKHuL72dWGx7qVP3j+5Hyxpiah#a0H2ET#aw4K7AdwOa+rLWew1LwxDJOITc3dsbaW4jTb0+9we#r71hJ4SstO+Ja6ta+bKVUiVYYgqQN1CY6EEH1zT#FeoJa3P2SO1FtsJbCH5SDzwK5MJTWKq8nRbnXi6qoU7p6mzYPZ2uif2FaSCK02GLe672YnvXLjwHYaN4h0+fQh9o1WJDLcLLFtRoycFm9c9h7Vp+EFi1GadpSWWJMlV6ml8S+JpbZlFmjwOpAEzDBGP4fpXVWwHPU9lS0fU5KGNlCDnV+Qy#wDEMdpr7h3E0KEK+wYA9cDt9Kh8W6rpV7pa3dpcl5TLsCjtxySK4C8v3nuHlcjczFiR696pNcEnkk17tPAQjKM07OKPP9tKSaa0ZckuMk56VD52TzVQynpQsnFd6SMlDQvrL0NXraXnrj1rHWTtmr1pMqyozjcoYFh0yPSk+4mrI9N8MSSWjw3E2yLeNiM#Vl64+leT#FfUvDupXU0cMFzb61HKXl3N5iMOmAew7#jXe3r2viKGG6jklgk0+PItmb5Jh#d+uKqzfCbRBrQ1a432+kpCLgtJJmQsedrr2xnFfG4nm9tJSjZo+gwqhGlFqVz53OOP1ptamvWSWOs3UUTB4RIdjBSARntmsys1tc6LCUUUUCCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAcuMc17B8L08X2WkGXTra2Oh3HmSSySYBLrgbSevpge9ePqSOQa+jfBfh2fSfAlncCW5iNzEZGglkzEQed6g9PpTiuaSV7E1JcsHK1zH8VQNZ3iIyeXI8SvIg6Kx6ge1cjcTsM4Yg+oODXb6r4f1i6Rrr7NLMoBIfPUDv7iuHuoiCeK+uwso+z5VLma3PAa967VkzJnYs1U3q7MpBPt1qnIK6XbY6okB61HUrdaiqDZDW617l+zn#wAzL#26#wDtWvDT1r3L9nP#AJmX#t1#9q1w5j#u0vl+aNqXxI8Fb7x+tJTm+8abWwwpc0lFMQtLmkopgLRRRQIKWkooAWjNFFMAzS5pKWmhC0ZpKKYDgaU0ynCi4hRTu1Npc1SYDgKAaAaKZLHCnqcVGOKcKExMlBp61EpqRTVIhlhM8VbhHPNU4znFdBoen294zG4vIraNOWLDJx7ChySVzCbsjR8P2Nld3AgvJGh3jEcg6K3q3tXoQsdM8M6WiXscF9eA7ljJ4TPfPcVneGfDa2dwbub7NdWqxllVW3MR1BC1k+KNXhv70zW8ckfAUh2yM#TtXDUbrVeSL06nMnpdnTWPiLw9YQNJFYsZ5WAeJ2yo9x6UvibxgRcXNknMbbWjcHBXjkZHUV5hJc4Y#wBO9QtdMSCSTgYyTVrA0+fnepSnPlsj1jwz4hmTT7q6n#e2tnHwmMkMehx#WuG1LVmmvpJ4yybmLAbslfxqjpHiO50eR3hc7XUqyZ4b61lSXBckk5yaqnhoxqSlbcLSdk+hrXeqz3soknlZ3AC5Y5OBUcc5JHNZHnc9amjlJIrp5UlZC5LHa+HNPm1e+W2gK7wNxyeg9a9D07TINLWV576JoipjJV8ZJ45rlfhvNc+YQLVHtXJUTHCmNvY9xVTxRZ3djcSb45FidyEY87q8nERdaq6LlZfmXBqklNK50CeJNO068k0pJFjsIIykO8lgZB3J6n615zqGpTXM5aWdpSMqrE9qzri5bcTuP51RefJx#Ku3DYOnh#gVhTnOrrI6XRvEU+jXn2qFUeQLja5O0+5Fb3iDxiNT8MQQloZbmeRmn+XBix0x7V5x53HWmmfJrSeGpzmptaoa5rWvoXJJsk85qAyH1qAyZ6U3ea2tpYOUseZTg+KrbzTw9Nu4WLaSVaies5Wq1A2Tik1fQiS0Om0m5mhl3RMdxwPXP4V3g1KSDTnu9Qt57uHIjMUa7mIP8se9Y#gjSN9o99dWZKH#AFEjHAJ7g0y61DxHqtlqtjpVu1rc797HdiSQKoUBF#iHc18zmmNiqns0te534DBufvuWi6HnXxL1nwlrrKNJE0F5aARqpX92UH8OfXNeZEfnXoD#AAv16TxItiRFLIzK8uxuVyeQQOhrI8f+HIvDXiq7sbZt9spGGHIDY5GfrXlxa2R60jlKKXBpKokKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiilCkjOOKAJrV0juI5JF3IjBivrjtXRaj4#8SalqH2t9SliVcLFBGcRxoOigenH41d8E+CpfFOieILiFGaeytw8Cj+Ns8j8q5Ka1ntpXjmhdHX7yspGKWjY7aXPffhd4rk8R2mo3Or3QfU4nDCeeQIgUjARR0#DFakng9b#AFS8udYgZgYTKiR#JuPavOfCXwq1DVdGTVLi8fT5ElWVYmBBkj7MvbPpXudg8SCYR391diPYGaYgkADoK0w2InScvZbdWc2Ko05tOTszw3XfDN7plol9NGscMzHYhb94o7ZFcnIpBr2bxIfDes3zSXd7eC6dCAvAWMjoDXj10uyR1BB2nGR3r67D1ZVIXnuebB+80Um9aiNSvxUZrVnShh617l+zn#zMv#br#wC1a8NPWvcv2c#+Zl#7df8A2rXBmP8Au0vl+aNqXxI8Gb7xpppT94#WkrUYUUUUwClpKKYhaWkooAWigUUwCiiigQtLTaWmAtFJQOlAhaKTvS0wHUtM6UuaYDgacDTe1KDVXEOpwNMBpR60IlkgNSKeahBqQGrRLLEZrQtnOR046dqzY+taNojO4C8knAAGc1SfQ56lranongoNuuLtvMIjiKqIzlw544HesjxJZnTb5ovtEU+erxnv7irvhq1OmyNqd8Xt4LbHXIZmPQD1PesjxLBLDeGZpPPjn#eJMBgSZ5#AiuSKftnK5y3TaRhyS81AZKjkkyTzmoi5rrOiMSfzaQy1XLe9G73oK5SwJKkSbHfFU9x9aUORzQHKdBp+q3No6GKeSPYfl2t098dK9Dl14aT4aEGqS#a5LpAY4xy0aEckN0zXkSTbT1q3capPcwwxSybkgXYgPasatL2jXN0MnBp2RJcTKXO0nbnjPpVQyVC0uepphf3rYuMbExkzSbxUO6jOaLlWJt9G+ocmlBoCxOGp4eq4NODUCsWVbB61ZjkI5#yaoq#NTI1BDR0thrd7aQPbw3UiQvgMoYkYzn8K9F0bVDrFvY3D3KWt5bykLLGwB24G4MOp3cflXkELnita0mZWVgxyO4PNcGMwNPERs9H3FTryoSvE9V+32g8QSXAjhNwzjfOvU46c1xPjDRNc8bzXH2x4dP0+wDSy#IMMf4TnuTxVjR1kurhYg3zHuTjFdBceM9J0nRnlaSC+tt5W4hdsHaONwB+9zXi5hh6VJqN#eO3A1qs29LrufME8MlvO0UqMjKcEMMH24qKu48b6#wCHfFVyb7TrKXT74cOGO6OVe2O4NcPXno9ISiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAqSKN5HRI1Znc7VUdz6U2tvw1e6bpWr299rFlNeWsZysUb7NzeufagPU9m+HUtlonh5re2#tKDUPLLXVtdJtQnOCy#4VvwxaR4huryynsI3W+iEcgEYyFXoV7g0Xt0+u+Ho9Vt4o4Yp03hQwdmRQOpHfGOK4GTUp7WRjDM0TYxuQ#pXq4LBwxNHfU8vE16lOv7uiO717WbfTtGi023u0leM+VDsGPLQdm96o+F9XjFzIFu1hvCuLZZQTG7noG9q88kujuJJOScnnNEV2Q2N2M16dPL4U8O6KZy1Ksp1fbHX+O#D19G1zrGI#ILKJNjDaXx8xX2z+NeWz9favRPFGtfZNB0#TobpTJ5JF1bg71BboSfX+VecStziunDKSp2kXTWtyButRGpCeaj7VozpQw9a9z#Zz#5mX#t1#wDateGd69y#Zz#5mX#t1#8AatcOY#7tL5fmjel8SPBW+8frQKG+8frSVoMdSdqKKYBRS0lMApc0lFMQtApKWmAtFJRQAtFFFAhe1FJS07gKKKSg0XAWlpoNL3p3ELTu1NoBNNCH5pwPFMFLVITHing1GCKdmmJlhG##AFetdZ4Xf7NJJeSPFHCoI3Sd2xwBXHqxB4qZZ2ChcnA5A7VW5hUhzKx0F5rt3cqUmuHdN24Bj39qz5r+WWIQtKxQHIBPSs8yE00vxjNCSREaSRM0mTTC1R7jSbqZrYkLUm6o91GaQ7Eu6lDVDnmlzQKxMHp2+oA1G6ncLE27mjdUW6jNFxWJd1JupgNGaAsSbqcGzUWaUNQBIGp4aoQ1SA0yWiUGpUbpVYHmplbpQS0XoicjH6niug0ywubpS8UEjRr95wuVX61zkJycZ9+a9R8BjVba0mEVo5sbvGZG6ADvXPiavsocy3MXHmlbY6PTNBtIbtRbCRmigWWYqcjBH8J#vV5L8Wr7SLiCys9Oia2khzm2lixKMk5YnvnrXsGqtqMN5A9iNpaF4Xu0GDCvqF7kdqyP+FfaTcX+m6tLeR6nvRvtF3KTukPYgDpj0r4mWInXqe9G7jf1Pfp0oUYNp6Ox8vgFiAASTwBXZeJvBk2leGtF12MEx30X71D#AAuDjivS4vAfh6LxZMUs7qK1SAq0jw5Bc#ddAOPeuy1iwn1Pw1DoeleVNJCpiE06jftxglT0BrSF6icoLYJzhBpN7nycaK7Dx14Pi8Kap5Fvf293FgD5ZAXDY5yPrXI4FNa7DG0UUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRTwNxAVcknGKAJIYxJKqO+xCRufGdo7nivoG18FeHpfCuh288trdeQ#mLcLGR5kTdmH96sP4a+Djplump6pp9ve2V#G0MySqQ1sRzgg+vFbuomz0+3a3sGk2PIZH3tkL2wPaunC4aVerFNe6c2JxMaUNHqbdpplhoq3F7piyx6dbJIBZQyb9wP8bZ6H2ryq+mVpXK52kkrk9s1qz6tdRW81vHMyRzD51B+8Peuenfk17+AwMcLzJO9zzK2IeIkpSWyIJJeahaY0kje9VmY8816Ow4xCSUnJzk1Xc5pXPNRseals2ikMY0w9KUmmmoNEhpr3P8AZz6+Jf8At1#9q14Yele5#s5#8zL#ANuv#tWuHMP92l8vzRvS+JHgrfeP1pKVvvH60lagFKKSimAtFGaKACiiimAUZoopiFooopgFLSUZoAWiiigQtFJQKAFpaSimAuaKTNLmncQtOBptFCYD80oPamDmlzVITRIDTgajBp1VclofuPrRuplGaETYfuo3UzNGadwsPzmjNNzRmgLD93tS7qj3GlBoAfmjNMzS0XAfmjNMpc0BYeDQDTM0uadxWH5pajzSg0XFYkFPVqhBp4piaJgakVqrg81IDQQ0XYpMHrXcWXxAvxpk1hOkbwugWIR#J5ZHGeK8+V8GrKSEd+aipThUtzIzaPT9C8dz2tp5M3mSzghYGzwg9#XNdrcWl4mmytG5aIqHjto0wICeTz3zXg0M5Qgg4I54rpW8ZaxO25r11GzywqcALjFebictjKrGpS0ad#8AgDjWnCDpyd0zfn166cCB532IThQec1o2N5Kuj3l7CJ2ntSJEEJ5LDt7gjqK4KO6Jxlie+e9aun6lPbMDFMyZ9DxW2JwiqUnCOjZhSquFRTlqkSWngGLxd4oj1m8KQrJIJZbJk2bIfX#a59K868beFodG1+5i0uQ3lsuZWaJDsiBPAzXtllrtxIU6Ag7snv6##qrVs#Ddje6VqFpb7rc37gyyMRwBywz6HmvnamDqUI3lrY9injadWTSXofKBFNr1fxz8IL7TJZL7QvJvLLG4xwOCyL2OO#FeVuhRirAhgcEHqK51JPY62hlFLikpiCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKB1pQM07bx3+lADR16c12#g0+E9EmGq+J3kvJY+YNNgXOT6u3QfSub1LRbrR4rb7chinuIxKkbcMqHoSO2azc459aW6Hqj6NtPip4f8AEkkVjDb#AGSWXEccMj7VLdix6AY71YudFtdUid9Mv47h8tgAYRyv3lDngkV817ua9Y+HvxD1O30qDw1Bpf24NMBux8sKHqeP1NbU8VVofC9DnqYWnVu2tQvraWPcSpwDgtjgH61h3CkZHP1r6AudHt5tINjdWKMqjzvLt5Mq7egP614n4g0q50rUHt7q2a3c#OsZOcKemD3r6XBY6GJTS6HkyoyotJ9TnZKrvVmUVVeu81iRN1qM08nioicVDNkNpppxppqWUhp6V7n+zl#zMv8A26#+1a8MJr3P9nL#AJmX#t1#9q1wZh#u8vl+aNqXxI8Gb7x+tJSt94#WkrYAooooAKWkoFMBaKKWgBKKKKYBS0lFMQtFFFAC5opKWmAUUUUCAUtJRQAtFJS0wFpaSjNMQtLTaXNNCHUuaZmlzTuFh2aXNMzS0XFYfkUZpv4UU7hYfmk603NLmgLDsUdKaDS0xWFzS5ptFArDs0ZpMijIouA4UtNz6UuaAHZpRimUtMQ8EUvIpgIpwYU0IkBpwNRA04E5polonU1Ipx3qupqUGghotI#NWY3NUFarMbUzKUTShc9K1bLLFaxYTk8V2HhDUDYaouLdJhNiNldd2PcVlWk4wckYuN5WOt0rw7c28qMRHIxTeq5+UtjgE9q4v4jeLNR0JLfTLqO3kvxFvimt3Km3ZuoPZuK9J1DSr7WEv7CG8lgiRRJClvhTIxH3WJ7#ANK+bfGtjeaZ4iksr#UPt00S4Mu7OP8AZz7dK+LqYmeJnefQ9#D4anRj7u7#AAMifWNRuJvOe9n3n0cjHsPaqzTNcyAzuST1Y9aiY5NABp7Gly3f6Zdac8aXMRQSKHjfHDqehBqpjr7V754C0G18bfC5dP1WHz5bJi1tKANwUn#Vhux4#DNebeKfh7qWgX8dtGouJpVaQ28J3vAo6ByOM4qObuO19jiqKe0bo5R1KsOqkYIpuKoQlFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRS4oASijGKXBwDQAlKBmjaauppV7#AGZJqJt5BZJIsbS7eNx6CgCC2tprq6jt7eNpZpCFRFGSx9MV7J8Mfhlbz6mt#rww1pLiSykGCrfwk9iKt+GPA3hu88Gw6nYS3S3xmSVJrlfLMbAc4I+8v0rsDrsytCktx9oljAV5QoHmH1rbD0JVpO2yOfEYiNGPmeKfFl5pviFqFxIcpIQI#QKOAB24x2rhq90+JXhca7p8OoWUM82pSTCK0t7dcoI+rEjsck5rxi+0fUNMnMF5aSxOGKDKnkj0PeueOnuvdHTe65kUgK9N+CVlqk#jNp9Pk8qKGI#aJGj3ptPY#XFcLo+h6lrWoRWVjaySSuQPunC5OMn2rUuINf8ABviCfTLaa5ilikG7yQwEmO+O4pT1TiVG61PfNf1DUdMmla3ykTgqDj5RnrivM9Xurm#aNZ5Wl8sbUL9QPTNevrcrq3gm2u3R9RiuIgWZhjnHTA6YNcdpXhL+19Q2zrItqud7oOuO31r6LLsTSdH2kopWPAxNKUKvJe55dOmOapSfzr0DxVbeHzZj+yZDHPASsiyD5pCOMj2rgJRgfWvWhLnjzWKhJvRlZqjapGqJqbOhDT0pKU03NQy0NNe6fs5f8zL#ANuv#tWvC690#Zy#5mX#ALdf#atcOYf7vL5fmjWn8SPBm+8frSUH7x+tFajCiiimIKKKKYBS0lFAC0UUUAFFFFMAooooELRSUtMAFLSUUCFopBS0wClpKKAFopKWmAtFNpRTELRRRQAuaXNNzS0xC5pc02jNADqM0lAp3AXNLmkpc0XEGaXNNzRmmOw#ijim5pc0CsLS5pCaTNMVhwNOzTAaXNArDxSimA04GmJocKcKYKcDQKw#NSqahB5p4qiWiwp5qxGaqKelWoTg0zKSNS1haRgqglsdB1rodJ860uopoiUlRsg+9a#w2ubB7zyLuzjzAGnF0D8w4xg+1dlHo2k6jZb9Os2WHa0n2ksPv5+4R19683E4yNKXs5xsvwMVSlV1i9ewaNqM91FLdX9yEtw2JHJ6Z4JNeN#Fa78N3GpxWulW7w3VuNpdWDRyDPXPv1zXt+mWS6ZDJLdQiS3VfNYqNwYDuPUV55q3w3XxhdXniNLhRYyAm324jLAHowHTPavmcbUj9YvfS2lv1PawMH7F30dzw2WzuYWG+CQbhlfl4I9jWv4Y8LX3ifXY9LgxHIxG7fwQPXB619IJ4d0U6NpFnIiv9nKNmWIB3A5CH296rzaHo6eNbPUbIzrc7pGmmEZHA+7sIGMA8VhKpKMU5LRnRHllJpPYqeG4YND0maEJi8tm+ySTRZSKQL0Kr#e7E1ft7rTrd7nWWs1e6CEPJnJ2nqceo96o+LJ5LeeNmmUrNllQH7v5cVgWesvbO4GGVxtZWGQR6GvboYBzwtr6vW541TFtYnm6GDpvw7fxZq2q6lf3gksvLd4njI80Y6fJXH3#AMNvEdrYjUItPlms2UuHAwVXOBn34r2#R9Qje4gSG3ht8AoDGuMA9vpXEfFnXtZ1HSoDCt3BYLIYpACVUsp9BXm1aE6FlUerPSo4iNdvkWiPGHRkcq6lWHUHtTcV03gi0t9V8TW9jfwSXFnMcXATllX+8PcE11fij4Rz6Z4jg0rS7rz5blmZEIzsQD5cnuTWfN3NrHltFa+seH9T0O+Syv7fy7hhuEQYM34gdPpWUylWIYEEdQR0piG0UUUAFFFFABRRRQAUUUUAFFFKOtACUuKntrWe8mWG2hkllboiKSa2PD3hifxFrB0mK6t7e8JIVJ2xuI7A9M0XQGDUvkSLCszRsI2OFYjg#T1r2XQPhLZ2XimfTNcMjpGkc0dwgygP8SP2IPTNY#xj0e5i8RQTWlk0GnrEIbaBF+6q#wAQA7H1pX6gmr2W4vw68HeENcZJL7XQ92v37J4iqnORjPc5r0230rT9L8Of8I#qESXsdvKZIYiwQH0Vj3xzXkPwo0S6vPGIAvDYPCpPzEBi2OBhu2a9N8QLdRRReed9yiHz3Vfl3ZrpwlGNaq6cuxzYyrOlBSi#kP8AJTw5Z3Si6iNpOmLK1QEiPPLYPpXMm#IfOe#QVQu7yRyAzk7eAD2+lUDcZPJr6PB4KOHhypnkV60q8uaSsz0rTvGCuIBcIySwH9y8DbQvHIPrmneI#Ctt401nRNSlneGGNij+SBiN87hlT2Pc1xvh2a3fVYftVzDBAjb3aXJBA7cV6CPGWi2+rLp1v5f2F2y04PygY6V5WYYBNtUI+9u#68zqwuKnBr2j0Whcvbyy0S9W5is4UvhH5JmjQKJU9cdKnkvNFE0WoXD2zXiRMSWAJYuO#wBK4HxD4wGrwrAsCq0MjBJl#iTtWBHeMWGT+taU8ohOknNWfl1InjaiqNxd0eu6ZqlnfX8bQwPFOUMZ8s4QjvlemfenaxFejTWh0Ex7Y3JkCth8+nvXNeCby3F8UmCLK3MMrc4b0rG8Raxd6T4mnmCvEyyGRY2bt71MMCliXGkrW19SZYiU6V6mrOX1vR9Sgldri0mUsxJLLwT7VyM42k8Y5r0W18c38t6Vv7kNbyBg2VB2Z#iFefahIJLmVw24Fjg+ozXuQc9pfgTS0dig9RHrT2PNR5qmdiGmmGnGkqGWhpr3T9nH#mZv+3X#ANq14Wa91#Zy#wCZl#7df#atcGYf7vL5fmjSn8SPBW+8frQKG+8frSVsMWikpaACiiimIKKKKAClFJRTAWlpBRQAUUUUwCiiigQoopKKAFooopiFopKWmAUUUUAKKKSigBaKKKYBS0lFMQ6k70UUALRSUZpgFLSUtAC0uabRmgQ7NLmm0tO4C0oOKbmlzTCw7rS0wdaXPvQKw6lzTQaB0pktEgNKDzUYNOBoAkBp+aiBpwqrk2LCGrMX3qpo2DVy2BdwByScAeppmUkbVgzq+VJGeDg4zXpnhCLWQCId6W7EBy6#KB9KzfC3hWC7sonvrZ7WeBt0qyN#r19AOoq1qvjprd5rawjkiVjsdJTkBAMAAdsV5+Jm637qmr930RzRspcz+R6C8RkiMSSKIwQJokk2g45AX0z3FUNZnktozJbBERT88SADy2POCOlcnp2vxQ+CLl3uITcvLhEJ+Yjuau6N4ui1Cwi08ssV2GUrPJF5isc9CPp3rxY5fOhKVWMeZX19PI7pYqNZKnJ27PzMe61udb4XEjl5A2fmPXHappfHjS2V5HKpWWRf9HMRxs9jVbx3bQ22szG2ZnV#mYBMKh9M1wk03zEZr3KeHo14xm4nBF1YSaTNCa9eRvmck#7RzTY7nkZNZJmPrTkmIOc128iVkiOTqepeFY7WbTXkDwyXYOdjvt2Y6DPv7UeO4R4i0m204Nd2szyJDLZbVXGeTLk#eHbNcr4Pj+3a5BCJ#JxlvM#u49a7jVb7w#8A2gj3zh721fYmw9d38X09RXzGa4as6v7v3vLsergK1KC99W#Uo2vgyw0DStPeOW3gv7aXzLqa1O5nA4Rc9gRya27HXY5Lh7iWNnZQUQxoDIu4Y+WsbxVfRaXFHb2qWkSTLuYQdee#0Ncna6o0Fyjh3AUgnaefwrXCYByw7ct2Y4nFv2yt8KK1#wCCLLUfHoli1JyiRrK73GfMMuejL1H4V0#xG8O6JcaPez2lvDFqtwqGS48olBtHOwj7ufenf8JHpv8AaM99BpiJcSIF80#eJ9frUEGuSr5gJDrJ99H5BH0rnp5XXcX7R69Doq5lSjJci06nJav8MdPg8GaXf2kpbULhV81lyYlXPLZ9apal8H76G#u4NPuGnjht0mjZoyDLnGQMdua9NtdWlkwuQEPAQL8o9OK6Wy1Forc3FxMERF4BYc#7I9TU1cFOlHnnIIZhGpLlhE8D#wCFM+MXZxFYB8HGc4B+max9Z+HniDQIjJqkNvbAdnuEyfoM5r0r4h#GO+jMuk6HK9sy#LJJ1deOhPTP0rxG8vrrULhp7y5lnlY5LyMWJri95vR6HoJq2qGzwmEgFkb3U5p8Fo8+wI0Y3HHzOBj61X70Zq#Qk7ix+E#i3UYVns7KGeFv44p1Yfoasn4O+Ko4ppJ7URqi7h3LHOMfWuT0TxHq#h67S50u#mt3Ug4VztPsRX0B4J+LCeJbUW2qSJBeABS4OMe+O4+nSojdfEOV7e6jzuL4QzL#AG3Hc3xWSwgDxERna7EAlSfUZ6CtOX4aaQvw8a#Ehh1PC+Y0gJVcdSvsa9K1G#mjUOsm+OQZDDo#vWC+uSws+7bIrDBRhkY+lehDLpzjzKR5rzJKXK42a3LnhOz0qy0awk8qP+1Y7QwpeeSFRww4yP4setcjZ+BtF0fxnBJNdG5guYW2opKyGXPOzPT2NXJtaleZXLYCcKo6KPQVrXPi2zFnbXgt4JNVU#edM7BRWyuqox9nu9yqeYwc5OS06GhrurtE8SKZIyqhTG0gZlx6nvRpN7bX+sR3bxu7+V5UkLHdEy+pB6GvPrrUnuLl5W4LsWIzWpoHimTRZXZYI5RJw2##ABr062XRlQUOXmaOCniJRq88XZPc6eXQNG0HX49bhMV#K7ZvV8sscN#qyuOAQav+JNbj0m1ljvYkuJLyM#KvAj46Ad#rU9lqd5#wjEurC2gESOZBHkBSK868QeMn1rTmtZYIwxm8xZf4lX+7mvMwOX1XWcpu8UzuxOMhKmlBavqc5POSeuffFVTLgnmopJck#TrUDOK+rVraHBGBbE+KX7Scf0qhv96Xfz1oK5C+s5z1qzBOdwwRnPFZAk96njlNLoJw0PW#D7Wz6b52hrE2pIUeYX4PlRRg#PjH8XpXIeNrqO61qaaC8e6iYZR3GCoz936Cl8L6xqFjdCKyLP5xAaLGQ#1rR8YwabHa3UtjarLKDi4O#H2djzgD0964YUnTxDlLW5HPoo22POJpSTyapSNnNSyt1wQRng561WYiu1s7IxsMY80wmnE0zioZrEaetJ2pT1ptSWIa91#Zx#5mX#t1#wDateFdq91#Zx#5mb#t1#8AatcOYf7vL5fmjSn8R4M33j9aSlb7x+tJWoBRmiimAtFApRzQISiiimAUUUUAFLmkopgLRSZp1ACUUtJTAKKKKBC0UlGaYC0ZpM0tABmlpKKYhaKTNLQAUUUUALRxSUUALRmiimAdaWkFGaYhaKTNLmgBaKTNGaAFzRSUUwHUopopc0CFpaaDSg00AtOptLmmJi0opM0d6Yh+acpqOnA0ySZTirMEzROro2GByCO1UgcVIG96aZLjc6FfEWoPcCeS7laUAAsW5IHQGl1LW59UvZLufaHkIJCDArADmnCT0o5Y3vYxdJGot0dwOTx0rp#B#iF9N1iIGWCOKVgJJZVzsA9D2zXDh#epFlOMZ4NKcIzjysTg1qj0PxJ4+vNTkvbaPyfskp2fKvUA8EHtXEvKSeSPwqmZSSMmk30qdKNNWihez6ss+Zz1p6yYPWqe40ofmtB8pox3LJ0Zh64OM1YF2x6sSfU1lCQ1Ir+9KxDgahu3ZtzOS2MZJ7elPSf35rNVyamR6DNwNSKY1oW0uepNY0LEkVp2nzc4OOlTJWMpKx1+iWzyXMIdDgn061Q+KGtajoGkxJJp9gIruFolRjmaAk#eBBwc4#Cu10aNtV0u1svtG1WjKzyQHa6KOgzXz58R4WsPEctiupS3sKEsm#OI+cYGevSvkMfXdat7NrRHu4CjGnTdRNNv8DjmYscsSSepJzTc0maKwOoXNGaSigBQavaTql1o2pw6hZuq3EDZUsu4fl3qiKUUWvoB9N6Tq1lrWh2kX9swXd#LAHeJiBIJPTjgD0Fc#rNrPYXbwXC7JB2z0rO+C19oVrp16uoNZ29zI3lJK7#vHyOMD29a6vxbHPdPAqW2VVP3csa5Mw9cjrXoZVWnGp7JvQ83MaMbKa3OEmmIJ5qlJP15qa5BVyCCGBxgjHNZ0r8mvqEebFXVx7zH1pgnIPXNVmbiomeg2ULm9P4lvn0mLTVl8u1jBBRON+f73rWHLMWJ96hZyelRlsnrSjFR2RagOZye9MJphbFMLGmaJEhb3pN1Rk03NFx2JwwzUiSYPrVTdShyKLg4na+HtXsNIje7luHad42iEcYwy5H3s1zNzfyMJAsjbHJzz1+tUDKelMZyepyfWpSSbkTGlrcHfJ4qInmlZs1GaTZukBNNNBNNJqblpATSGikJqWMK91#Zx#5mb#t1#wDateFV7r+zj#zMv#br#wC1a4sf#u8vl+aNKfxHgzfeP1pKVvvH60lagFFFFABS5pKKYC0UUUAFFFFMQUUUUAFLmkopgLmikpaACiiigAooopiCiiimAtFFFFwCiiigBaKSlpiCiiigAooooAKWkopgLRRRRcAzRmiigQtApBS0wFopKKAFzS5pKKYhc0tJS00AtKKTNJTAfS00GlBoJaHg0oao6cDTFYlDUoJHpUQNODU7k2Jd1KHqLNKCKYrEwegPUWfelzTFYm3U4NUGeKcGoEThqeGqANTwfSgloso9To9U1NToelMzkjRgbnjr#OvSvDnhrTtT0kzwXjyXbJkQ4x5Z759RXmELYYV2vg7UbWw1FpbqeaJAvyCIffPofauTFxqSg3TeplHl5ve2Ox1e11nT9BnTRIRF5NszTzsv+sfsIz2IPrXzz4xOvvqcMviNCt9JCDlsbmXsTivpm38QW93ciOBS1sTll5wfbHYV5Z8bPCmqh08RzuZ0c7THGoCwJ#CD3zXyVWFWnNSq7y#A9zD1Kc4uNNfD+J4rRS4oosaiUUUUgFpVpBThmmB6Z8JvCWm+I7ma4urgreWkiyQQ#wAMyj7wP4V77bQ2lsrLpiHYiMYhI2RGSei+gHevIfhP4r0S0tovDUenzTXtw283BZV+f0UnoB711#imDUNLmmaGSZYujup+7ntV4WhCvUabtJbHNjKs6cVp7rOI8VWV1YatNHeOksj#AL0yIcq4PpXLytya1r93dsuSfTnOKx5T1r7KmmoJM8eDTZXdqiZqV2qJmqzoSAtTC1IWphNI0SFJppNJn1ppakUkOzSE00mkzSHYdupM0wk0nNK47D91NLetJmkJpDsGaQmkJppNIqwUmaWm5qRhmikpaQxK92#Zx#5mX#t1#wDateE17t+zh#zM3#br#wC1a4sf#u8vl+aLp#EeDN94#WkoPU#WitgCiiigAooooAKKKKYC0UCigAooopiCiiigAooooAWikpRTAKKKKACiiimAUUUUCDNLSUCmAtFFFABS0lFMBaKSloEFFFFABRRRQAtFJRmncBaBRRRcBaKSloEApaSimAtGaKKAFopKUGmIWlFNzS5p3Ad2pabmlBpiFzSg0gpcUyRwNKDUeaUGgCTNLmmZozTESg4p2c1EDzT+tMVh6mpFaoQaeDTuS0ToasRniqitxViI89R9fSmZS0NCAE81sWakEdT6irGgeG7y9vbTzbWYW8zf6zHVe5HpXXXfguWzYy2skdzbl9qeWcnGe9c9TE04vlvqc01J6o6Lw1p8OmWMepzXBNvLF8xC5aPjr#8AXrwjxzd65qXiC4lj#tRtPZ#Lg+0Z+Ye#Y175o2mh#D8kUkk8AMn7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This code is heavy because it contains an image.

A frame has been already defined in this figure, in order to have a frame adapted to the picture of the set of Mandelbrot

In the palette color, activate the magenta color (the background color of the image is black, so we won’t use a black point).

Use icon (expanding the points toolbar) to create a free point and get it named C.

Now use icon (by expanding the measures toolbar) to measure the complex affix of point C. A dialog box pops up to enter the name of the measure : enter c and validate.

We must first create a complex function of a complex variable. For this use (expanding the calculations toolbar) icon . Fill in the dialog box as shown underneath and validate :

Let us now create the recurrent sequence. For this use in the calculations toolbar icon .

Fill in the dialog box as shown underneath :

Now we have to create the graph of this sequence.

For this use icon in the locuses toolbar.

A dialog box pops up. Fiil it in as shown here :

.

With the capture tool you can now move point c and see that when point C remains in the black part (set of Mandelbrot), ths sequence semms to be convergent (with sometimes pretty patterns !).

You can see the figure underneath and you can capture point C :

To be noted :

With palette tool you can change the style, color and point style of the graph. ths display will be faster with a continuous line style than a doted one.