https://wiki.unissula.ac.id/index.php?action=history&feed=atom&title=Permukaan_Brown
Permukaan Brown - Riwayat revisi
2026-09-16T04:13:44Z
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https://wiki.unissula.ac.id/index.php?title=Permukaan_Brown&diff=9182&oldid=prev
Maintenance script: Presentation V4: sitasi, referensi, Math, Wikimedia Commons, dan atribusi
2026-08-25T04:08:36Z
<p>Presentation V4: sitasi, referensi, Math, Wikimedia Commons, dan atribusi</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Revisi sebelumnya</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revisi per 25 Agustus 2026 04.08</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Baris 1:</td>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''Permukaan Brown''' adalah [[permukaan fraktal]] yang dibuat melalui [[Fungsi (matematika)|fungsi]] ketinggian [[fraktal]].</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[File:Brownian_surface.png|thumb|right|280px|Brownian surface]]</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''Permukaan Brown''' adalah [[permukaan fraktal]] yang dibuat melalui [[Fungsi (matematika)|fungsi]] ketinggian [[fraktal]].<ins style="font-weight: bold; text-decoration: none;"><ref>John C. Russ. [https://books.google.com/books?id=qDQjyuuDRxUC&pg=PA167&dq=%22brownian+surface%22&hl=en&ei=1vXyTK_mGobtsgbcp6CYCw&sa=X&oi=book_result&ct=result&resnum=4&ved=0CDAQ6AEwAw#v=onepage&q=%22brownian%20surface%22&f=false Fractal Surfaces, Volume 1]. 1994. hlm. 167. ISBN 0-306-44702-9.</ref><ref>Heping Xie. [https://books.google.com/books?id=lXElMU9_tIMC&pg=PA73&dq=%22brownian+surface%22&hl=en&ei=1vXyTK_mGobtsgbcp6CYCw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCMQ6AEwAA#v=onepage&q=%22brownian%20surface%22&f=false Fractals in Rock Mechanics]. 1993. hlm. 73. ISBN 90-5410-133-4.</ref><ref>Tamás Vicsek. [https://books.google.com/books?id=InnD-GTUi0gC&pg=PA40&dq=%22brownian+surface%22&hl=en&ei=1vXyTK_mGobtsgbcp6CYCw&sa=X&oi=book_result&ct=result&resnum=9&ved=0CEkQ6AEwCA#v=onepage&q=%22brownian%20surface%22&f=false Fractal Growth Phenomena]. 1992. hlm. 40. ISBN 981-02-0668-2.</ref></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Seperti [[gerak Brown]], permukaan Brown dinamai dari botanis abad ke-19 [[Robert Brown]].</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Seperti [[gerak Brown]], permukaan Brown dinamai dari botanis abad ke-19 [[Robert Brown]].</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Contoh ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Contoh ==</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Misalkan, dalam kasus tiga dimensi, dengan ''X'' dan ''Y'' sebagai koordinat permukaan Brown, fungsi ketinggian antara titik (''x''<sub>1</sub>, ''y''<sub>1</sub>) dan (''x''<sub>2</sub>, ''y''<sub>2</sub>) dapat diatur untuk memiliki rata-rata atau [[nilai harapan]] yang bertambah seiring [[Vektor (spasial)|jarak vektor]] antara (''x''<sub>1</sub>, ''y''<sub>1</sub>) dan (''x''<sub>2</sub>, ''y''<sub>2</sub>). Namun, ada banyak cara untuk mendefinisikan fungsi ketinggian. Misalnya, variabel [[gerak Brown pecahan]] () dapat dipakai atau berbagai fungsi rotasi dapat dipakai untuk membuat permukaan yang lebih alami.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Misalkan, dalam kasus tiga dimensi, dengan ''X'' dan ''Y'' sebagai koordinat permukaan Brown, fungsi ketinggian antara titik (''x''<sub>1</sub>, ''y''<sub>1</sub>) dan (''x''<sub>2</sub>, ''y''<sub>2</sub>) dapat diatur untuk memiliki rata-rata atau [[nilai harapan]] yang bertambah seiring [[Vektor (spasial)|jarak vektor]] antara (''x''<sub>1</sub>, ''y''<sub>1</sub>) dan (''x''<sub>2</sub>, ''y''<sub>2</sub>).<ins style="font-weight: bold; text-decoration: none;"><ref>John C. Russ. [https://books.google.com/books?id=qDQjyuuDRxUC&pg=PA167&dq=%22brownian+surface%22&hl=en&ei=1vXyTK_mGobtsgbcp6CYCw&sa=X&oi=book_result&ct=result&resnum=4&ved=0CDAQ6AEwAw#v=onepage&q=%22brownian%20surface%22&f=false Fractal Surfaces, Volume 1]. 1994. hlm. 167. ISBN 0-306-44702-9.</ref> </ins>Namun, ada banyak cara untuk mendefinisikan fungsi ketinggian. Misalnya, variabel [[gerak Brown pecahan]] () dapat dipakai atau berbagai fungsi rotasi dapat dipakai untuk membuat permukaan yang lebih alami.<ins style="font-weight: bold; text-decoration: none;"><ref>Heping Xie. [https://books.google.com/books?id=lXElMU9_tIMC&pg=PA73&dq=%22brownian+surface%22&hl=en&ei=1vXyTK_mGobtsgbcp6CYCw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCMQ6AEwAA#v=onepage&q=%22brownian%20surface%22&f=false Fractals in Rock Mechanics]. 1993. hlm. 73. ISBN 90-5410-133-4.</ref></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Pembuatan permukaan Brown pecahan ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Pembuatan permukaan Brown pecahan ==</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Pembuatan permukaan Brown pecahan () yang efisien menemui berbagai tantangan. Karena permukaan Brown menggambarkan [[proses Gauss]] dengan fungsi peragam nonstasioner, metode [[dekomposisi Cholesky]] dapat dipakai<del style="font-weight: bold; text-decoration: none;">.</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Pembuatan permukaan Brown pecahan () yang efisien menemui berbagai tantangan.<ins style="font-weight: bold; text-decoration: none;"><ref>Kroese, D.P. ''Spatial Process Generation''. ''Lectures on Stochastic Geometry, Spatial Statistics and Random Fields, Volume II: Analysis, Modeling and Simulation of Complex Structures, Springer-Verlag, Berlin''. 2015. hlm. 369–404. doi:10.1007/978-3-319-10064-7_12.</ref> </ins>Karena permukaan Brown menggambarkan [[proses Gauss]] dengan fungsi peragam nonstasioner, metode [[dekomposisi Cholesky]] dapat dipakai.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Metode yang lebih efisien adalah metode Stein. Metode ini membuat proses Gauss stasioner dengan pendekatan ''circulant embedding'', lalu menyesuaikan proses tersebut untuk mendapatkan proses Gauss nonstasioner yang diinginkan. Gambar di bawah menunjukkan tiga perwujudan umum permukaan Brown pecahan untuk nilai kekasaran atau [[parameter Hurst]] yang berbeda. Parameter Hurst selalu di antara nol dan satu</del>.</div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Metode yang lebih efisien adalah metode Stein.<ref>Stein, M. L. ''Fast and exact simulation of fractional Brownian motion''. ''Journal of Computational and Graphical Statistics''. 2002. Vol. 11 (3). hlm. 587–599. doi:10.1198/106186002466.</ref> Metode ini membuat proses Gauss stasioner dengan pendekatan ''circulant embedding'', lalu menyesuaikan proses tersebut untuk mendapatkan proses Gauss nonstasioner yang diinginkan. Gambar di bawah menunjukkan tiga perwujudan umum permukaan Brown pecahan untuk nilai kekasaran atau [[parameter Hurst]] yang berbeda. Parameter Hurst selalu di antara nol dan satu.</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Lihat pula ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Lihat pula ==</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l16">Baris 16:</td>
<td colspan="2" class="diff-lineno">Baris 17:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[Gerak Brown pecahan]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[Gerak Brown pecahan]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>== <del style="font-weight: bold; text-decoration: none;">Rujukan </del>==</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>== <ins style="font-weight: bold; text-decoration: none;">Referensi </ins>==</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><references /></ins></div></td></tr>
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<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">== Sumber dan atribusi ==</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Konten artikel ini diadaptasi dari [https://id.wikipedia.org/w/index.php?title=Permukaan+Brown&oldid=17427527 Wikipedia bahasa Indonesia], revisi 17427527 (2020-09-22T03:55:34Z), yang tersedia berdasarkan lisensi Creative Commons Atribusi-BerbagiSerupa (CC BY-SA). Gambar pada artikel ini bersumber dari Wikimedia Commons dan mengikuti ketentuan lisensi masing-masing berkas. Mohon gunakan konten dan media secara bijak serta sesuai dengan ketentuan lisensi yang berlaku.</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">== Sumber dan atribusi ==</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><!</ins>-- <ins style="font-weight: bold; text-decoration: none;">WIKI_UNISSULA_PRESENTATION_V4 </ins>--<ins style="font-weight: bold; text-decoration: none;">></ins></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Konten artikel ini diadaptasi dari [https://id.wikipedia.org/w/index.php?title=Permukaan+Brown&oldid=17427527 Wikipedia bahasa Indonesia], revisi 17427527 (2020</del>-<del style="font-weight: bold; text-decoration: none;">09</del>-<del style="font-weight: bold; text-decoration: none;">22T03:55:34Z), yang tersedia berdasarkan lisensi Creative Commons Atribusi</del>-<del style="font-weight: bold; text-decoration: none;">BerbagiSerupa (CC BY</del>-<del style="font-weight: bold; text-decoration: none;">SA). Mohon gunakan konten ini secara bijak serta sesuai dengan ketentuan lisensi yang berlaku.</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
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Maintenance script
https://wiki.unissula.ac.id/index.php?title=Permukaan_Brown&diff=8783&oldid=prev
Maintenance script: Impor teks terkontrol dari Wikipedia bahasa Indonesia; revisi 17427527; atribusi sumber disertakan.
2026-08-25T03:42:03Z
<p>Impor teks terkontrol dari Wikipedia bahasa Indonesia; revisi 17427527; atribusi sumber disertakan.</p>
<p><b>Halaman baru</b></p><div>'''Permukaan Brown''' adalah [[permukaan fraktal]] yang dibuat melalui [[Fungsi (matematika)|fungsi]] ketinggian [[fraktal]].<br />
<br />
Seperti [[gerak Brown]], permukaan Brown dinamai dari botanis abad ke-19 [[Robert Brown]].<br />
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== Contoh ==<br />
Misalkan, dalam kasus tiga dimensi, dengan ''X'' dan ''Y'' sebagai koordinat permukaan Brown, fungsi ketinggian antara titik (''x''<sub>1</sub>, ''y''<sub>1</sub>) dan (''x''<sub>2</sub>, ''y''<sub>2</sub>) dapat diatur untuk memiliki rata-rata atau [[nilai harapan]] yang bertambah seiring [[Vektor (spasial)|jarak vektor]] antara (''x''<sub>1</sub>, ''y''<sub>1</sub>) dan (''x''<sub>2</sub>, ''y''<sub>2</sub>). Namun, ada banyak cara untuk mendefinisikan fungsi ketinggian. Misalnya, variabel [[gerak Brown pecahan]] () dapat dipakai atau berbagai fungsi rotasi dapat dipakai untuk membuat permukaan yang lebih alami.<br />
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== Pembuatan permukaan Brown pecahan ==<br />
Pembuatan permukaan Brown pecahan () yang efisien menemui berbagai tantangan. Karena permukaan Brown menggambarkan [[proses Gauss]] dengan fungsi peragam nonstasioner, metode [[dekomposisi Cholesky]] dapat dipakai.<br />
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Metode yang lebih efisien adalah metode Stein. Metode ini membuat proses Gauss stasioner dengan pendekatan ''circulant embedding'', lalu menyesuaikan proses tersebut untuk mendapatkan proses Gauss nonstasioner yang diinginkan. Gambar di bawah menunjukkan tiga perwujudan umum permukaan Brown pecahan untuk nilai kekasaran atau [[parameter Hurst]] yang berbeda. Parameter Hurst selalu di antara nol dan satu.<br />
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== Lihat pula ==<br />
* [[Proses Wiener]]<br />
* [[Gerak Brown pecahan]]<br />
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== Rujukan ==<br />
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== Sumber dan atribusi ==<br />
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Konten artikel ini diadaptasi dari [https://id.wikipedia.org/w/index.php?title=Permukaan+Brown&oldid=17427527 Wikipedia bahasa Indonesia], revisi 17427527 (2020-09-22T03:55:34Z), yang tersedia berdasarkan lisensi Creative Commons Atribusi-BerbagiSerupa (CC BY-SA). Mohon gunakan konten ini secara bijak serta sesuai dengan ketentuan lisensi yang berlaku.</div>
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