 the son of Husayn Bayqarah, who was a great-great-grandson  of the man historically known as Amir Timur and Tamerlane, was the ruler of where?
Herat
Timur
Timur (Persian: تیمور‎ ‎ "Temūr", Chagatai: "Temür "; 9 April 1336 – 18 February 1405), historically known as Amir Timur and Tamerlane (Persian: تيمور لنگ‎ ‎ "Temūr(-i) Lang", "Timur the Lame"), was a Turco-Mongol conqueror.
 As the founder of the Timurid Empire in Persia and Central Asia he became the first ruler in the Timurid dynasty.
 According to John Joseph Saunders, Timur's background was Iranized and not steppe nomadic.
Badi' al-Zaman Mirza
Badi' al-Zaman Mirza (Persian: بدیع الزمان‎ ‎ ; died 1514) was a Timurid ruler of Herat from 1506 to 1507.
 He was the son of Husayn Bayqarah, who was a great-great-grandson of Timur Beg.
Gur-e-Amir
The Gūr-i Amīr or Guri Amir (Uzbek: "Amir Temur maqbarasi, Go'ri Amir" , Persian: ‎ ‎ ), is a mausoleum of the Asian conqueror Timur (also known as Tamerlane) in Samarkand, Uzbekistan.
 It occupies an important place in the history of Persian-Mongolian Architecture as the precursor and model for later great Mughal architecture tombs, including Gardens of Babur in Kabul, Humayun's Tomb in Delhi and the Taj Mahal in Agra, built by Timur's Persianised descendants, the ruling Mughal dynasty of North India.
 It has been heavily restored. Musakhel, Punjab
Musakhel (Urdu: ‎ ), all hilly and green, is hard to be traced in the historical descriptions as there is no isolated account of the area available.
 However, by studying the history of Kandahár and northern Balochistan little can be ascertained about Musakhel.
 According to the early history, this area, being a part of Kandahár province, has been ruled by the Ghaznavids, Maliks of Kurat Dynasty, Amir Timur and his successors (1383-1470 AD), Sultan Husain Mirza of Herát (1470-1480 AD), and Amir Shuja-ud-Din Zunnún (1480-1504).
 In 1505 AD, the Mughals conquered the province of Kandahár and held it till 1559 AD when the Safavid Kings of Persia acquired it.
 The Mughals regained the province in 1595 AD but lost it again in 1622 AD, to the Safavid Kings of Persia.
 This time, the Safavids, conferred the government of Pishin and its tribal dependencies upon Sher Khan Tarin.
 He, after 7 years, refused to submit to the governor of Kandahár and became semi-independent, but had to retreat later on.
 In 1709 AD, the Afghan inhabitants rose under Mir Wais Ghilzai and established the Ghilzai power in Kandahár.
 The Ghilzai power was terminated by Nadir Shah in 1737 AD.
 After the assassination of Nadir Shah in 1747 AD, the first democratic government was established in Kandahár by the Afghans as they elected Ahmed Shah Durrani as their ruler.
 In 1826, the first Amir of Afghanistan, Dost Muhammad Barakzai, took hold of the area and annexed it to Afghanistan. Kamāl ud-Dīn Behzād
He was born and lived most of his life in Herat, a city in south-west of Afghanistan, during the time of the Timurids, and later in Tabriz under the Safavid dynasty.
 An orphan, he was raised by the prominent painter Mirak Naqqash, and was a protégé of Mir Ali Shir Nava'i.
 His major patrons in Herat were the Timurid sultan Husayn Bayqarah (ruled 1469 - 1506) and other amirs in his circle.
 After the fall of the Hamad, he was employed by Shah Ismail I Safavi in Tabriz, where, as director of the royal atelier, he had a decisive impact on the development of later Safavid painting. Jameh Mosque of Nishapur
The Jāmeh Mosque of Nishapur (Persian: مسجد جامع نیشابور‎ ‎ - "Masjid-e-Jāmeh Neyshabur") is the grand congregational mosque (Jāmeh) of Nishapur city, within Nishapur County, Khorasan.
 The mosque was founded by Pahlavan Ali Karkhi in 1493 during the rule of Husayn Bayqarah of the Timurid dynasty, and was rebuilt during the rule of Abbad I of the Persia Sultanate. Amir Timur Museum
The Amir Timur Museum is located in Tashkent, the capital of Uzbekistan.
 It opened in 1996, and is dedicated to the Mongol warlord Amir Timur (Tamerlane). Sultan Husayn Mirza Bayqara
Sultan Husayn Mirza Bayqara (Persian: حسین بایقرا‎ ‎ / "Husayn Bāyqarā") was born in Herat in June–July 1438 C.E. to Ghiyas ud-din Mansur Mirza son of Bayqarah Mirza I son of Umar Shaikh Mirza I son of "Amir" Timur Beg Gurkani.
 He was the Timurid ruler of Herat from 1469 until May 4, 1506, with a brief interruption in 1470. Tamerlane (poem)
"Tamerlane" is a poem by Edgar Allan Poe which follows a fictionalized accounting of the life of a Turkic conqueror historically known as Tamerlane.
 The poem was first published in the 1827 collection Tamerlane and Other Poems.
 That collection, with only 50 copies printed, was not credited with the author's real name but by "A Bostonian."
 The poem's original version was 403 lines but trimmed down to 223 lines for its inclusion in "Al Aaraaf, Tamerlane, and Minor Poems". Abu Sa'id Mirza
Mirza Abū Saʿīd Baig Mohammed Khan or Abū Saʿīd Mirza (Chagatay/Persian: ابو سعید میرزا‎ ‎ ) was the son of Muḥammad son of Miran Shah son of Amir Timur (Herat, 1424–1469), and was a Timurid Empire ruler in Transoxiana, Khurasan and the southern Caspian region, what is today parts of Turkmenistan, Kazakhstan, Uzbekistan, Iran, Azerbaijan and Afghanistan.
 He was a member of the Timurid dynasty.