"ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭ ᠠ"-ны өөр хувилбарууд

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92-р мөр: 92-р мөр:
=ᠬᠡᠷᠡᠭᠯᠡᠭᠡ=
=ᠬᠡᠷᠡᠭᠯᠡᠭᠡ=


== ᠹᠷᠠᠻᠲᠠᠯ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ==
== ᠹᠷᠠᠻᠲ᠋ᠠᠯ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ==
ᠮᠠᠨ᠍ᠳᠧᠯᠪᠷᠣᠲ ‍ᠤᠨ<sup>Mandelbrot</sup> ᠣᠯᠠᠨᠯᠢᠭ ᠪᠣᠯ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠬᠠᠪᠲᠠᠭᠠᠶ ᠳ᠋ᠤ ᠡᠭᠦᠰᠬᠡᠳᠡᠭ ᠹᠷᠠᠻᠲ᠋ᠠᠯ ‍ᠤᠨ<sup>fractal</sup> ᠲᠦᠭᠡᠭᠡᠮᠡᠯ ᠵᠡᠰᠱᠢᠶ ‍ᠡ᠋ ᠶᠤᠮ᠃   
ᠮᠠᠨ᠍ᠳᠧᠯᠪᠷᠣᠲ ‍ᠤᠨ<sup>Mandelbrot</sup> ᠣᠯᠠᠨᠯᠢᠭ ᠪᠣᠯ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠬᠠᠪᠲᠠᠭᠠᠶ ᠳ᠋ᠤ ᠡᠭᠦᠰᠬᠡᠳᠡᠭ ᠹᠷᠠᠻᠲ᠋ᠠᠯ ‍ᠤᠨ<sup>fractal</sup> ᠲᠦᠭᠡᠭᠡᠮᠡᠯ ᠵᠡᠰᠱᠢᠶ ‍ᠡ᠋ ᠶᠤᠮ᠃   


ᠡᠨᠡ ᠬᠦ ᠣᠯᠠᠨᠯᠢᠭ ᠠᠨᠤ z = 0 ᠡᠴᠡ ᠡᠬᠢᠯᠡᠭᠡᠳ ᠢᠲ᠋ᠧᠷᠠᠼ ᠬᠢᠬᠦ ᠳ᠋ᠦ <math>f_c(z)=z^2+c</math> ᠹᠦᠨ᠍ᠻᠼ ᠲᠣᠭᠲᠠᠪᠤᠷᠢ ᠲᠠᠢ ᠪᠠᠢᠢᠬᠤ ᠨᠥᠬᠦᠴᠡᠯ ᠪᠦᠬᠦᠢ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠᠨ ‍ᠤ ᠣᠯᠠᠨᠯᠢᠬ ᠪᠠᠢᠢᠳᠠᠭ᠃  
ᠡᠨᠡ ᠬᠦ ᠣᠯᠠᠨᠯᠢᠭ ᠠᠨᠤ <span style="writing-mode: horizontal-tb;"><i>z = 0</i></span> ᠡᠴᠡ ᠡᠬᠢᠯᠡᠭᠡᠳ ᠢᠲ᠋ᠧᠷᠠᠼ ᠬᠢᠬᠦ ᠳ᠋ᠦ <span style="writing-mode: horizontal-tb;"><i>f<sub>c</sub>(z)=z<sup>2</sup>+c</i></span> ᠹᠦᠨ᠍ᠻᠼ ᠲᠣᠭᠲᠠᠪᠤᠷᠢ ᠲᠠᠢ ᠪᠠᠢᠢᠬᠤ ᠨᠥᠬᠦᠴᠡᠯ ᠪᠦᠬᠦᠢ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠᠨ ‍ᠤ ᠣᠯᠠᠨᠯᠢᠬ ᠪᠠᠢᠢᠳᠠᠭ᠃  


ᠮᠠᠨ᠍ᠳᠧᠯᠪᠷᠣᠲ ‍ᠤᠨ<sup>Mandelbrot</sup> ᠣᠯᠠᠨᠯᠢᠭ ᠠᠨᠤ ᠪᠠᠢᠢᠭᠠᠯᠢ ‍ᠢᠢᠨ ᠭᠠᠢᠢᠬᠠᠮᠰᠢᠭᠲᠤ ᠳᠦᠷᠰᠦ ᠪᠠ ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲᠢᠭ᠌ ‍ᠦᠨ ᠰᠠᠢᠢᠬᠠᠨ ᠲᠣᠮᠢᠶᠠᠨ ‍ᠤ ᠶᠡᠷᠦ ᠪᠤᠰᠤ ‍ᠢᠢᠨ ᠭᠣᠶᠤᠮᠰᠠᠭ ᠬᠣᠣᠰᠯᠠᠯ ‍ᠢ ᠢᠯᠡᠷᠬᠡᠶ᠋ᠢᠯᠡᠳᠡᠭ᠃<ref>ᠷᠡᠨᠴᠡᠨ ‍ᠦ ᠡᠩᠬᠡᠪᠠᠲᠤ᠃ '''ᠫᠢᠲ᠋ᠾᠠᠭᠣᠷ ᠪᠠ ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲᠢᠭ᠌'''᠃ ᠮᠣᠩᠭᠤᠯ ᠤᠯᠤᠯᠰ ᠊ᠤᠨ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ‍ᠤ ᠠᠻᠠᠳᠧᠮᠢ᠃ ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲᠢᠭ᠌ ᠪᠠ ᠲᠣᠭᠠᠨ ᠲᠧᠻᠨᠣᠯᠣᠭᠢ ‍ᠢᠢᠨ ᠬᠦᠷᠢᠶᠡᠯᠡᠩ᠃ https://imdt.ac.mn/c/1013874?content=1150891&fbclid=IwAR1HVqeXwT-h7dijj9EeIUzDvFustH99GAr9LHYQIU61XIByuBHCkSm10So 2020</ref>  
ᠮᠠᠨ᠍ᠳᠧᠯᠪᠷᠣᠲ ‍ᠤᠨ<sup>Mandelbrot</sup> ᠣᠯᠠᠨᠯᠢᠭ ᠠᠨᠤ ᠪᠠᠢᠢᠭᠠᠯᠢ ‍ᠢᠢᠨ ᠭᠠᠢᠢᠬᠠᠮᠰᠢᠭᠲᠤ ᠳᠦᠷᠰᠦ ᠪᠠ ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲᠢᠭ᠌ ‍ᠦᠨ ᠰᠠᠢᠢᠬᠠᠨ ᠲᠣᠮᠢᠶᠠᠨ ‍ᠤ ᠶᠡᠷᠦ ᠪᠤᠰᠤ ‍ᠢᠢᠨ ᠭᠣᠶᠤᠮᠰᠠᠭ ᠬᠣᠣᠰᠯᠠᠯ ‍ᠢ ᠢᠯᠡᠷᠬᠡᠶ᠋ᠢᠯᠡᠳᠡᠭ᠃<ref>ᠷᠡᠨᠴᠡᠨ ‍ᠦ ᠡᠩᠬᠡᠪᠠᠲᠤ᠃ '''ᠫᠢᠲ᠋ᠾᠠᠭᠣᠷ ᠪᠠ ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲᠢᠭ᠌'''᠃ ᠮᠣᠩᠭᠤᠯ ᠤᠯᠤᠯᠰ ᠊ᠤᠨ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ‍ᠤ ᠠᠻᠠᠳᠧᠮᠢ᠃ ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲᠢᠭ᠌ ᠪᠠ ᠲᠣᠭᠠᠨ ᠲᠧᠻᠨᠣᠯᠣᠭᠢ ‍ᠢᠢᠨ ᠬᠦᠷᠢᠶᠡᠯᠡᠩ᠃ https://imdt.ac.mn/c/1013874?content=1150891&fbclid=IwAR1HVqeXwT-h7dijj9EeIUzDvFustH99GAr9LHYQIU61XIByuBHCkSm10So 2020</ref>  


ᠮᠠᠨ᠍ᠳᠧᠯᠪᠷᠣᠲ ‍ᠤᠨ  ᠹᠷᠠᠻᠲᠠᠯ ‍ᠤᠨ ᠵᠠᠭᠠᠭ ‍ᠢ ᠳᠠᠪᠠᠬᠤ ‍ᠳᠤ ᠪᠠᠨ ᠵᠦᠯᠢᠶ ‍ᠠ᠋ ‍ᠢᠢᠨ<sup>Julia</sup> ᠹᠷᠠᠻᠲᠠᠯ ‍ᠤᠳ ᠦᠷᠭᠡᠯᠵᠢ ᠬᠣᠯᠪᠤᠯᠲᠠ ᠪᠠᠨ ᠠᠯᠳᠠᠵᠤ᠂ ᠹᠠᠲᠣᠤ ‍ᠢᠢᠨ<sup>Fatou</sup> ᠲᠣᠭᠤᠰᠤ ᠪᠣᠯᠤᠨ ᠬᠦᠪᠢᠷᠠᠳᠠᠭ᠃
ᠮᠠᠨ᠍ᠳᠧᠯᠪᠷᠣᠲ ‍ᠤᠨ  ᠹᠷᠠᠻᠲ᠋ᠠᠯ ‍ᠤᠨ ᠵᠠᠭᠠᠭ ‍ᠢ ᠳᠠᠪᠠᠬᠤ ‍ᠳᠤ ᠪᠠᠨ ᠵᠦᠯᠢᠶ ‍ᠠ᠋ ‍ᠢᠢᠨ<sup>Julia</sup> ᠹᠷᠠᠻᠲᠠᠯ ‍ᠤᠳ ᠦᠷᠭᠡᠯᠵᠢ ᠬᠣᠯᠪᠤᠯᠲᠠ ᠪᠠᠨ ᠠᠯᠳᠠᠵᠤ᠂ ᠹᠠᠲᠣᠤ ‍ᠢᠢᠨ<sup>Fatou</sup> ᠲᠣᠭᠤᠰᠤ ᠪᠣᠯᠤᠨ ᠬᠦᠪᠢᠷᠠᠳᠠᠭ᠃





16:50, 2 Аравдугаар сар 2021-ий байдлаарх засвар

ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰcomplex ᠲᠣᠭ᠎ ‍ᠠ᠋ ᠨᠢ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭ᠎ ‍᠋ᠠ᠋ ‍ᠢᠢᠨ ᠣᠯᠠᠨᠯᠢᠭ ‍ᠢ ᠥᠷᠭᠡᠵᠢᠯᠦᠯᠵᠦ᠂ ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ‍ᠢ ᠰᠢᠢᠳᠦᠯ ᠲᠡᠢ ᠪᠣᠯᠭᠠᠭᠰᠠᠨ ᠣᠯᠠᠨᠯᠢᠭ ᠶᠤᠮ᠃

ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭ᠎ ‍ᠠ᠋ ‍ᠢᠢ a + bi ᠬᠡᠯᠪᠡᠷᠢ ᠪᠡᠷ ᠢᠯᠡᠷᠡᠬᠡᠢᠢᠯᠡᠵᠦ ᠪᠣᠯᠬᠤ ᠪᠡ ᠡᠭᠦᠨ ᠳᠦ ᠨᠢ a ᠪᠣᠯᠤᠨ b ᠨᠢ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭ᠎ ‍ᠠ᠋᠂ i ᠨᠢ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ ᠪᠢᠭᠡᠳ i2 = −1 ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ‍ᠦᠨ ᠰᠢᠢᠳᠦᠯ ‍ᠢ ᠬᠠᠩᠭᠤᠭᠰᠠᠨ ᠤᠳᠬ ‍ᠠ᠋ ᠲᠠᠢ ᠪᠠᠢᠢᠨ᠎ ‍ᠠ᠋᠃


ᠳᠦᠷᠰᠦᠯᠡᠯ

ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭ᠎ᠠ ‍ᠢᠢᠨ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠨᠢ ᠬᠡᠪᠲᠡᠭᠡ ᠲᠡᠩᠬᠡᠯᠢᠭ ᠪᠠ ᠪᠣᠰᠤᠭ᠎ ‍ᠠ᠋ ᠲᠡᠩᠬᠡᠯᠢᠭ ᠡᠴᠡ ᠪᠦᠷᠢᠳᠦᠳᠡᠭ᠃

ᠬᠠᠭᠤᠷᠮᠠᠬ ᠲᠣᠭ᠎ ‍ᠠ᠋ ‍ ‍ᠢᠢᠨ ᠣᠯᠠᠨᠯᠢᠭ ᠪᠣᠰᠤᠭ᠎ ‍ᠠ᠋ ᠲᠡᠩᠬᠡᠯᠢᠭ ᠲᠦ ᠪᠠᠢᠢᠷᠢᠰᠢᠳᠠᠭ᠃

ᠬᠡᠪᠲᠡᠭᠡ ᠲᠡᠩᠬᠡᠯᠢᠭ ᠲᠦ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭ᠎ ‍ᠠ᠋ ‍ᠢᠢ ᠪᠠᠢᠢᠷᠢᠰᠢᠭᠤᠯᠳᠠᠭ᠃


ᠺᠣᠮᠫᠯᠧᠺᠰ ᠬᠠᠪᠲᠠᠭᠠᠶ ‍ᠢᠢ ᠲᠥᠯᠦᠭᠡᠯᠡᠵᠦ ᠪᠤᠶ ᠠᠷᠭᠠᠨ᠋ᠳ᠋ ‍ᠤᠨArgand ᠳᠢᠶᠠᠭ᠋ᠷᠠᠮ ᠳᠡᠭᠡᠷ ‍ᠡ᠋ ᠺᠣᠮᠫᠯᠧᠺᠰ ᠲᠣᠭ᠎ ‍ᠠ᠋ ‍ᠢᠢ ᠸᠧᠺᠲ᠋ᠣᠷvector ᠡᠭᠦᠰᠬᠡᠵᠦ ᠪᠤᠶ ᠬᠣᠣᠰ ᠲᠣᠭ᠎ ‍ᠠ᠋ ᠪᠠᠷ (a, b) ᠳᠦᠷᠰᠦᠯᠡᠨ ᠦᠵᠡᠭᠦᠯᠵᠦ ᠪᠣᠯᠤᠨ᠎ ‍ᠠ᠋᠃

ᠡᠭᠦᠨ ᠳ᠋ᠦ:
Re ᠢᠨᠦ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭᠠᠨ ‍ᠤ ᠲᠡᠩᠬᠡᠯᠢᠭ᠂
Im ᠢᠨᠦ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠲᠣᠭ᠎ ‍ᠠ᠋ ‍ᠢᠢᠨ ᠲᠡᠩᠬᠡᠯᠢᠭ ᠪᠣᠯᠬᠤ ᠠᠭᠠᠳ
i ᠢᠨᠦ i2 = −1 ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠳ᠋ᠦ ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠬᠤ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠨᠢᠭᠡᠴᠡ ᠮᠥᠨ᠃



ᠦᠢᠯᠡᠳᠦᠯ

ᠨᠡᠮᠡᠬᠦ

ᠬᠣᠶᠠᠷ ᠺᠣᠮᠫᠯᠧᠺᠰ ᠲᠣᠭ᠎‍ᠠ᠋ ‍ᠢᠢ ᠨᠡᠮᠡᠬᠦ ᠳ᠋ᠦ ᠪᠡᠨ ᠪᠣᠳᠠᠲᠤ ᠬᠡᠰᠡᠭ ‍ᠦᠳ ‍ᠢ ᠬᠣᠭᠤᠷᠤᠨᠳᠤ ᠨᠢ ᠨᠡᠮᠡᠵᠦ᠂ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠬᠡᠰᠡᠭ ‍ᠦᠳ ‍ᠢ ᠬᠣᠭᠤᠷᠤᠨᠳᠤ ᠨᠢ ᠨᠡᠮᠡᠨ᠎ ‍ᠡ᠋᠃[1]



ᠬᠣᠶᠠᠷ ᠲᠣᠭ᠎ ‍ᠠ᠋ ‍ᠢᠢ ᠨᠡᠮᠡᠬᠦ ᠦᠢᠯᠡᠳᠦᠯ ‍ᠢ ᠳᠦᠷᠰᠦᠯᠡᠭᠰᠡᠨ ᠢᠨᠦ᠃



ᠬᠠᠰᠤᠬᠤ

ᠨᠢᠭᠡ ᠺᠣᠮᠫᠯᠧᠺᠰ ᠲᠣᠭ᠎‍ᠠ᠋ ᠡᠴᠡ ᠨᠥᠭᠦᠳᠡ ᠺᠣᠮᠫᠯᠧᠺᠰ ᠲᠣᠭ᠎ᠠ ‍ᠢᠢ ᠬᠠᠰᠠᠬᠤ ᠳ᠋ᠦ ᠪᠡᠨ ᠪᠣᠳᠠᠲᠤ ᠬᠡᠰᠡᠭ ᠪᠠ ᠬᠠᠭᠤᠷᠮᠠᠭ ᠬᠡᠰᠡᠭ ‍ᠦᠳ ‍ᠢ ᠲᠤᠰ ᠪᠦᠷᠢ ᠬᠠᠰᠤᠶᠤ᠃[1]



ᠦᠷᠡᠵᠢᠬᠦ

ᠺᠣᠮᠫᠯᠧᠺᠰ ᠲᠣᠭ᠎‍ᠠ᠋ ‍ᠢᠢ ᠦᠷᠡᠵᠢᠭᠦᠯᠬᠦ ᠳ᠋ᠦ ᠦᠷᠡᠵᠢᠭᠦᠯᠬᠦ ᠦᠢᠯᠡᠳᠦᠯ ‍ᠦᠨ ᠰᠡᠯᠭᠦᠬᠦ (commutative)᠂ ᠪᠦᠯᠦᠭᠯᠡᠬᠦ (associatove)᠂ ᠵᠠᠳᠠᠯᠬᠤ (distributive) ᠴᠢᠨᠠᠷ ‍ᠤᠳ ᠦᠢᠯᠡᠴᠢᠯᠡᠳᠡᠭ ᠃[2]



2 + i ᠬᠡᠮᠡᠬᠦ ᠲᠣᠭ᠎ ‍ᠠ᠋ ‍ᠢᠢ (ᠴᠡᠩᠬᠡᠷ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ) ᠬᠢᠭᠡᠳ 3 + i ᠬᠡᠮᠡᠬᠦ ᠲᠣᠭᠠᠨ ‍ᠳᠤ (ᠤᠯᠠᠭᠠᠨ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ) ᠦᠷᠡᠵᠢᠭᠦᠯᠬᠦ ᠦᠢᠯᠡᠳᠦᠯ ‍ᠢ ᠳᠦᠷᠰᠦᠯᠡᠭᠰᠡᠨ ᠢᠨᠦ᠃

ᠤᠯᠠᠭᠠᠨ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ‍ᠢ ᠡᠷᠭᠢᠭᠦᠯᠵᠦ ᠴᠡᠩᠬᠡᠷ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ‍ᠤ ᠣᠷᠤᠶ ᠲᠠᠢ ᠲᠠᠭᠠᠷᠠᠭᠤᠯᠵᠤ᠂ √5 ‍ᠢᠢᠠᠷ ᠰᠤᠩᠭᠠᠨ᠎ ‍ᠠ᠋᠃ ᠡᠨᠡ ᠢᠨᠦ ᠴᠡᠩᠬᠡᠷ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ‍ᠤ ᠾᠢᠫᠣᠲ᠋ᠧᠨᠦᠽ ‍ᠤᠨhypotenuse ᠤᠷᠲᠤ ᠪᠣᠯᠠᠢ᠃



ᠬᠤᠪᠢᠶᠠᠬᠤ

ᠺᠣᠮᠫᠯᠧᠺᠰ ᠲᠣᠭᠠᠨ ‍ᠳᠤ ᠦᠢᠯᠡᠳᠦᠯ ᠭᠦᠢᠴᠡᠳᠬᠡᠬᠦ ᠳ᠋ᠦ ᠪᠡᠨ ᠬᠤᠪᠢᠶᠠᠭᠴᠢ ‍ᠢᠢᠨ ᠬᠣᠣᠰᠮᠠᠭ ᠲᠣᠭ᠎‍ᠠ᠋ ‍ᠢᠢ ᠠᠰᠢᠭᠯᠠᠳᠠᠭ᠃ ᠬᠤᠪᠢᠶᠠᠷᠢ ‍ᠢᠢᠨ ᠬᠣᠣᠰᠮᠠᠭ ‍ᠢᠢᠠᠷ ᠬᠦᠷᠲᠡᠪᠦᠷᠢ ᠪᠠ ᠬᠤᠪᠢᠶᠠᠷᠢ ‍ᠢᠢ ᠦᠷᠡᠵᠢᠭᠦᠯᠳᠡᠭ᠃



ᠻᠸᠠᠲᠷᠠᠲ ᠵᠡᠷᠭᠡ

ᠺᠣᠮᠫᠯᠧᠺᠰ ᠲᠣᠭ᠎‍ᠠ᠋ ‍ᠢᠢ ᠻᠸᠠᠲᠷᠠᠲquadrate ᠵᠡᠷᠭᠡ ᠳ᠋ᠦ ᠳᠡᠪᠰᠢᠭᠦᠯᠬᠦ ᠳ᠋ᠦ ᠪᠡᠨ ᠥᠪᠡᠷ ‍ᠢ ᠢᠨᠦ ᠥᠪᠡᠷ ᠲᠦ ᠢᠨᠦ ᠦᠷᠡᠵᠢᠭᠦᠯᠦᠨ᠎‍ᠡ᠋᠃[3]



ᠻᠸᠠᠲᠷᠠᠲ ᠢᠵᠠᠭᠤᠷ

ᠺᠣᠮᠫᠯᠧᠺᠰ ᠲᠣᠭ᠎ᠠ a + bi (b ≠ 0) ‍ᠢᠢᠨ ᠻᠸᠠᠲᠷᠠᠲ ᠢᠵᠠᠭᠤᠷ ᠠᠨᠤ ᠪᠠᠢᠢᠬᠤ ᠠᠭᠠᠳ ᠡᠭᠦᠨ ᠳ᠋ᠦ᠄ ᠪᠠ ᠪᠣᠯᠤᠮᠤᠢ᠃ sgn b ᠭᠡᠭᠴᠢ ᠢᠨᠦ ᠭᠡᠵᠦ ᠲᠠᠢᠢᠯᠠᠭᠳᠠᠨ᠎ᠠ᠃

ᠡᠭᠦᠨ ‍ᠢ ᠪᠠᠲᠤᠯᠠᠬᠤ ‍ᠢᠢ ᠲᠤᠬᠠᠢᠢᠲᠠ ᠳ᠋ᠤ ᠲᠣᠭ᠎ᠠ ‍ᠢᠢ ᠻᠸᠠᠲᠷᠠᠲ ᠵᠡᠷᠭᠡ ᠳ᠋ᠦ ᠳᠡᠪᠰᠢᠭᠦᠯᠵᠦ a + bi ᠲᠣᠭ᠎ᠠ ‍ᠢᠢ ᠭᠠᠷᠭᠠᠵᠤ ᠢᠷᠡᠬᠦ ᠶᠣᠰᠤᠲᠠᠢ᠃


ᠬᠡᠷᠡᠭᠯᠡᠭᠡ

ᠹᠷᠠᠻᠲ᠋ᠠᠯ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ

ᠮᠠᠨ᠍ᠳᠧᠯᠪᠷᠣᠲ ‍ᠤᠨMandelbrot ᠣᠯᠠᠨᠯᠢᠭ ᠪᠣᠯ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠬᠠᠪᠲᠠᠭᠠᠶ ᠳ᠋ᠤ ᠡᠭᠦᠰᠬᠡᠳᠡᠭ ᠹᠷᠠᠻᠲ᠋ᠠᠯ ‍ᠤᠨfractal ᠲᠦᠭᠡᠭᠡᠮᠡᠯ ᠵᠡᠰᠱᠢᠶ ‍ᠡ᠋ ᠶᠤᠮ᠃

ᠡᠨᠡ ᠬᠦ ᠣᠯᠠᠨᠯᠢᠭ ᠠᠨᠤ z = 0 ᠡᠴᠡ ᠡᠬᠢᠯᠡᠭᠡᠳ ᠢᠲ᠋ᠧᠷᠠᠼ ᠬᠢᠬᠦ ᠳ᠋ᠦ fc(z)=z2+c ᠹᠦᠨ᠍ᠻᠼ ᠲᠣᠭᠲᠠᠪᠤᠷᠢ ᠲᠠᠢ ᠪᠠᠢᠢᠬᠤ ᠨᠥᠬᠦᠴᠡᠯ ᠪᠦᠬᠦᠢ ᠺᠣᠮᠫ᠊ᠯᠧᠺᠰ ᠲᠣᠭᠠᠨ ‍ᠤ ᠣᠯᠠᠨᠯᠢᠬ ᠪᠠᠢᠢᠳᠠᠭ᠃

ᠮᠠᠨ᠍ᠳᠧᠯᠪᠷᠣᠲ ‍ᠤᠨMandelbrot ᠣᠯᠠᠨᠯᠢᠭ ᠠᠨᠤ ᠪᠠᠢᠢᠭᠠᠯᠢ ‍ᠢᠢᠨ ᠭᠠᠢᠢᠬᠠᠮᠰᠢᠭᠲᠤ ᠳᠦᠷᠰᠦ ᠪᠠ ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲᠢᠭ᠌ ‍ᠦᠨ ᠰᠠᠢᠢᠬᠠᠨ ᠲᠣᠮᠢᠶᠠᠨ ‍ᠤ ᠶᠡᠷᠦ ᠪᠤᠰᠤ ‍ᠢᠢᠨ ᠭᠣᠶᠤᠮᠰᠠᠭ ᠬᠣᠣᠰᠯᠠᠯ ‍ᠢ ᠢᠯᠡᠷᠬᠡᠶ᠋ᠢᠯᠡᠳᠡᠭ᠃[4]

ᠮᠠᠨ᠍ᠳᠧᠯᠪᠷᠣᠲ ‍ᠤᠨ ᠹᠷᠠᠻᠲ᠋ᠠᠯ ‍ᠤᠨ ᠵᠠᠭᠠᠭ ‍ᠢ ᠳᠠᠪᠠᠬᠤ ‍ᠳᠤ ᠪᠠᠨ ᠵᠦᠯᠢᠶ ‍ᠠ᠋ ‍ᠢᠢᠨJulia ᠹᠷᠠᠻᠲᠠᠯ ‍ᠤᠳ ᠦᠷᠭᠡᠯᠵᠢ ᠬᠣᠯᠪᠤᠯᠲᠠ ᠪᠠᠨ ᠠᠯᠳᠠᠵᠤ᠂ ᠹᠠᠲᠣᠤ ‍ᠢᠢᠨFatou ᠲᠣᠭᠤᠰᠤ ᠪᠣᠯᠤᠨ ᠬᠦᠪᠢᠷᠠᠳᠠᠭ᠃



ᠨᠡᠷ ‍ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠯᠠᠯ

ᠡᠬᠢ ᠰᠤᠷᠪᠤᠯᠵᠢ

  1. 1.0 1.1 ᠰᠡᠷᠳᠠᠮᠪᠠ ᠪᠥᠬᠡᠪᠠᠲᠤ᠃ ᠺᠣᠮᠫᠯᠧᠺᠰ ᠲᠣᠭ᠎ᠠ᠃ Geogebra. https://www.geogebra.org/m/CwryWtd9?fbclid=IwAR0i1VN-HH5hegFJoWMjgCM9si7zH7x9hHDuEbU6iROuW3gbqIAeMGngvAs#material/nLiRDrsU ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/08/17
  2. Виленкин Н. Я., Ивашов-Мусатов О. С., Шварцбурд С. И. Алгебра и математический анализ для 11 класса. Учебное пособие. — Изд. 6-е. — М.: Просвещение, 1998. — 288 с. — ISBN 5-09-008036-4.
  3. Math is Fun. https://www.mathsisfun.com/algebra/complex-number-multiply.html ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/09 01
  4. ᠷᠡᠨᠴᠡᠨ ‍ᠦ ᠡᠩᠬᠡᠪᠠᠲᠤ᠃ ᠫᠢᠲ᠋ᠾᠠᠭᠣᠷ ᠪᠠ ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲᠢᠭ᠌᠃ ᠮᠣᠩᠭᠤᠯ ᠤᠯᠤᠯᠰ ᠊ᠤᠨ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ‍ᠤ ᠠᠻᠠᠳᠧᠮᠢ᠃ ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲᠢᠭ᠌ ᠪᠠ ᠲᠣᠭᠠᠨ ᠲᠧᠻᠨᠣᠯᠣᠭᠢ ‍ᠢᠢᠨ ᠬᠦᠷᠢᠶᠡᠯᠡᠩ᠃ https://imdt.ac.mn/c/1013874?content=1150891&fbclid=IwAR1HVqeXwT-h7dijj9EeIUzDvFustH99GAr9LHYQIU61XIByuBHCkSm10So 2020