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"translatedText": "屏幕底部有一个完整视频的链接来回答这个问题。或者,供参考:https://youtu.be/LqbZpur38nw", | ||
"input": "A link to the full video answering this is at the bottom of the screen. Or, for reference: https://youtu.be/LqbZpur38nw" | ||
} | ||
] |
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{ | ||
"translatedText": "Mandelbrot 集是如何定义的", | ||
"input": "How the Mandelbrot set is defined" | ||
} |
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"translatedText": "Un lien vers la vidéo complète répondant à cette question se trouve en bas de l'écran. Ou, pour référence : https://youtu.be/LqbZpur38nw", | ||
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3b1b
Author
Owner
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"input": "A link to the full video answering this is at the bottom of the screen. Or, for reference: https://youtu.be/LqbZpur38nw" | ||
} | ||
] |
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{ | ||
"translatedText": "Comment l'ensemble de Mandelbrot est défini", | ||
"input": "How the Mandelbrot set is defined" | ||
} |
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1 | ||
00:00:00,000 --> 00:00:03,360 | ||
סט מנדלברוט הוא אחת התמונות האייקוניות ביותר בכל המתמטיקה. | ||
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2 | ||
00:00:03,780 --> 00:00:09,776 | ||
מתחילים במספר מרוכב כלשהו, c, ואז מגדירים באופן רקורסיבי רצף של מספרים | ||
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3 | ||
00:00:09,776 --> 00:00:16,280 | ||
מרוכבים שבו הרצף מתחיל ב-0, וכל ערך חדש מוגדר כריבוע של הערך הקודם, בתוספת c. | ||
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4 | ||
00:00:16,780 --> 00:00:21,283 | ||
אז, למשל, באיטרציה הראשונה, אתה לוקח 0 בריבוע פלוס c, | ||
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5 | ||
00:00:21,283 --> 00:00:27,956 | ||
כלומר z1 הוא רק c, ואז עבור האיטרציה הבאה, אתה לוקח את המספר הזה בריבוע פלוס c, | ||
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6 | ||
00:00:27,956 --> 00:00:31,960 | ||
כלומר z2 הוא c בריבוע פלוס c, וכן הלאה וכן הלאה. | ||
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7 | ||
00:00:32,180 --> 00:00:35,080 | ||
כל ערך חדש הוא הריבוע של הקודם פלוס c. | ||
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8 | ||
00:00:35,560 --> 00:00:41,540 | ||
בהתאם לבחירה עבור אותו ערך c, לפעמים הרצף נשאר מוגבל, ולפעמים הוא מתפוצץ עד אינסוף. | ||
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9 | ||
00:00:42,060 --> 00:00:46,655 | ||
אם אתה צובע את כל הערכים של c שגורמים לתהליך הזה להישאר מוגבל בשחור, | ||
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10 | ||
00:00:46,655 --> 00:00:49,786 | ||
ואתה מחיל קצת שיפוע של צבעים על הערכים האחרים, | ||
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11 | ||
00:00:49,786 --> 00:00:52,983 | ||
כאשר הצבע תלוי כמה מהר התהליך מתפוצץ עד אינסוף, | ||
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12 | ||
00:00:52,983 --> 00:00:56,380 | ||
אתה מקבל את האייקוני הקרדיואידי הזה -עם צורת בועות. | ||
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{ | ||
"translatedText": "קישור לסרטון המלא המשיב על כך נמצא בתחתית המסך. או, לעיון: https://youtu.be/LqbZpur38nw", | ||
"input": "A link to the full video answering this is at the bottom of the screen. Or, for reference: https://youtu.be/LqbZpur38nw" | ||
} | ||
] |
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[ | ||
{ | ||
"translatedText": "סט מנדלברוט הוא אחת התמונות האייקוניות ביותר בכל המתמטיקה.", | ||
"input": "The Mandelbrot set is one of the most iconic images in all of math.", | ||
"time_range": [ | ||
0.0, | ||
3.36 | ||
] | ||
}, | ||
{ | ||
"translatedText": "מתחילים במספר מרוכב כלשהו, c, ואז מגדירים באופן רקורסיבי רצף של מספרים מרוכבים שבו הרצף מתחיל ב-0, וכל ערך חדש מוגדר כריבוע של הערך הקודם, בתוספת c.", | ||
"input": "You start with some complex number, c, and then you recursively define a sequence of complex numbers where the sequence starts with 0, and each new value is defined to be the square of the previous value, plus c.", | ||
"time_range": [ | ||
3.78, | ||
16.28 | ||
] | ||
}, | ||
{ | ||
"translatedText": "אז, למשל, באיטרציה הראשונה, אתה לוקח 0 בריבוע פלוס c, כלומר z1 הוא רק c, ואז עבור האיטרציה הבאה, אתה לוקח את המספר הזה בריבוע פלוס c, כלומר z2 הוא c בריבוע פלוס c, וכן הלאה וכן הלאה.", | ||
"input": "So, for example, on the very first iteration, you take 0 squared plus c, meaning z1 is just c, and then for the next iteration, you take that number squared plus c, meaning z2 is c squared plus c, and so on and so forth.", | ||
"time_range": [ | ||
16.78, | ||
31.96 | ||
] | ||
}, | ||
{ | ||
"translatedText": "כל ערך חדש הוא הריבוע של הקודם פלוס c.", | ||
"input": "Each new value is the square of the previous plus c.", | ||
"time_range": [ | ||
32.18, | ||
35.08 | ||
] | ||
}, | ||
{ | ||
"translatedText": "בהתאם לבחירה עבור אותו ערך c, לפעמים הרצף נשאר מוגבל, ולפעמים הוא מתפוצץ עד אינסוף.", | ||
"input": "Depending on the choice for that value c, sometimes the sequence stays bounded, and sometimes it blows up to infinity.", | ||
"time_range": [ | ||
35.56, | ||
41.54 | ||
] | ||
}, | ||
{ | ||
"translatedText": "אם אתה צובע את כל הערכים של c שגורמים לתהליך הזה להישאר מוגבל בשחור, ואתה מחיל קצת שיפוע של צבעים על הערכים האחרים, כאשר הצבע תלוי כמה מהר התהליך מתפוצץ עד אינסוף, אתה מקבל את האייקוני הקרדיואידי הזה -עם צורת בועות.", | ||
"input": "If you color all of the values of c that cause this process to stay bounded black, and you apply some gradient of colors to the other values, where the color depends on how quickly the process blows up to infinity, you get this iconic, cardioid-with-bubbles shape.", | ||
"time_range": [ | ||
42.06, | ||
56.38 | ||
] | ||
} | ||
] |
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{ | ||
"translatedText": "כיצד מוגדר סט מנדלברוט", | ||
"input": "How the Mandelbrot set is defined" | ||
} |
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[ | ||
{ | ||
"translatedText": "इसका उत्तर देने वाले पूरे वीडियो का लिंक स्क्रीन के नीचे है। या, संदर्भ के लिए: https://youtu.be/LqbZpur38nw", | ||
"input": "A link to the full video answering this is at the bottom of the screen. Or, for reference: https://youtu.be/LqbZpur38nw" | ||
} | ||
] |
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{ | ||
"translatedText": "मैंडेलब्रॉट सेट को कैसे परिभाषित किया गया है", | ||
"input": "How the Mandelbrot set is defined" | ||
} |
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[ | ||
{ | ||
"translatedText": "Ссылка на полное видео с ответом на этот вопрос находится внизу экрана. Или для справки: https://youtu.be/LqbZpur38nw", | ||
"input": "A link to the full video answering this is at the bottom of the screen. Or, for reference: https://youtu.be/LqbZpur38nw" | ||
} | ||
] |
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{ | ||
"translatedText": "Как определяется множество Мандельброта", | ||
"input": "How the Mandelbrot set is defined" | ||
} |
i'm one of those willing to help translate videos because i highly support your channel. For some reason the AI translated " l' " by a series of numbers and symbols. idk wether or not it's normal. It seems to have done so for every other " l' ".