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==在科技上的应用==
 
==在科技上的应用==
 
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*分形晶体管
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*分形晶体管<ref name="Fractal transistor">{{cite journal| title=Fractal structures for low-resistance large area AlGaN/GaN power transistors| last1=Reiner |first1=Richard |first2=Patrick |last2=Waltereit |first3=Fouad |last3=Benkhelifa |first4=Stefan |last4=Müller |first5=Herbert |last5=Walcher |first6=Sandrine |last6=Wagner |first7=Rüdiger |last7=Quay |first8=Michael |last8=Schlechtweg |first9=Oliver | last10=Ambacher| first10=O.|last9=Ambacher |journal=Proceedings of ISPSD |year=2012 |isbn=978-1-4577-1596-9 |doi=10.1109/ISPSD.2012.6229091 |pages=341–344 }}</ref>
*分形换热器
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*分形换热器<ref>{{cite journal|author1=Zhiwei Huang|author2=Yunho Hwang|author3=Vikrant Aute|author4=Reinhard Radermacher|title=Review of Fractal Heat Exchangers|date=2016|url=http://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=2724&context=iracc|format=PDF|postscript='' International Refrigeration and Air Conditioning Conference''. Paper 1725}}</ref>
 
*数码影像
 
*数码影像
*建筑
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*建筑<ref name="springer.com 9783319324241"/>
*城市发展
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*城市发展<ref>{{Cite journal | last1=Chen | first1=Yanguang | title=Modeling Fractal Structure of City-Size Distributions Using Correlation Functions | doi=10.1371/journal.pone.0024791| journal=PLOS ONE | volume=6 | issue=9 | pages=e24791 | year=2011 | pmid=21949753 | pmc=3176775|arxiv = 1104.4682 |bibcode = 2011PLoSO...624791C }}</ref><ref>{{cite web |url=http://library.thinkquest.org/26242/full/ap/ap.html |title=Applications |accessdate=2007-10-21 |url-status=dead |archiveurl=https://web.archive.org/web/20071012223212/http://library.thinkquest.org/26242/full/ap/ap.html |archivedate=October 12, 2007 }}</ref>
 
*组织病理学切片分类
 
*组织病理学切片分类
 
*分形景观或海岸线复杂性
 
*分形景观或海岸线复杂性
*用分形分析探测“我们不知道的生命”
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*用分形分析探测“我们不知道的生命”<ref>[http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9012687&fileId=S1473550413000177 "Detecting 'life as we don't know it' by fractal analysis"]</ref>
 
*酶(米氏方程)
 
*酶(米氏方程)
 
*新型音乐的产生
 
*新型音乐的产生
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*价格系列的技术分析
 
*价格系列的技术分析
 
*网络中的分形
 
*网络中的分形
*医学
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*医学<ref name="medicine" />
*神经科学
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*神经科学<ref name="cerebellum" /><ref name="neuroscience" />
*影像诊断
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*影像诊断<ref name="diagnostic imaging" />
*病理学
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*病理学<ref name="pathology">{{Cite journal | last1=Smith | first1=Robert F. | last2=Mohr | first2=David N. | last3=Torres | first3=Vicente E. | last4=Offord | first4=Kenneth P. | last5=Melton III | first5=L. Joseph
*地质学
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| title=Renal insufficiency in community patients with mild asymptomatic microhematuria | journal=Mayo Clinic Proceedings | volume=64 | issue=4 | pages=409–414 | year=1989 | pmid=2716356 |doi=10.1016/s0025-6196(12)65730-9}}</ref><ref>{{Cite journal | last1=Landini | first1=Gabriel | title=Fractals in microscopy | doi=10.1111/j.1365-2818.2010.03454.x | journal=Journal of Microscopy | volume=241 | issue=1 | pages=1–8 | year=2011 | pmid= 21118245| pmc=}}</ref>
*地理位置
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*地质学<ref>{{Cite journal | last1=Cheng | first1=Qiuming | authorlink=Qiuming Cheng| title=Multifractal Modeling and Lacunarity Analysis | journal=Mathematical Geology | volume=29 | issue=7 | pages=919–932 | doi=10.1023/A:1022355723781 | year=1997 | pmid= | pmc=}}</ref>
*考古学
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*地理位置<ref>{{Cite journal | last1=Chen | first1=Yanguang <!-- editor is irrelevant here| editor1-last=Hernández Montoya | editor1-first=Alejandro Raúl -->| title=Modeling Fractal Structure of City-Size Distributions Using Correlation Functions | doi=10.1371/journal.pone.0024791 | journal=PLOS ONE | volume=6 | issue=9 | pages=e24791 | year=2011 | pmid=21949753 | pmc=3176775|arxiv = 1104.4682 |bibcode = 2011PLoSO...624791C }}</ref>
*地震学
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*考古学<ref name="archaeology">{{cite journal | last1=Burkle-Elizondo | first1=Gerardo
*搜索和救援
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| last2=Valdéz-Cepeda | first2=Ricardo David | title=Fractal analysis of Mesoamerican pyramids | journal=Nonlinear Dynamics, Psychology, and Life Sciences | volume=10 | issue=1 | pages=105–122 | year=2006
*技术分析
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| pmid=16393505}}</ref><ref>{{Cite journal | last1=Brown | first1=Clifford T. | last2=Witschey | first2=Walter R. T. | last3=Liebovitch | first3=Larry S. | title=The Broken Past: Fractals in Archaeology | doi=10.1007/s10816-005-2396-6 | journal=Journal of Archaeological Method and Theory | volume=12 | pages=37–78 | year=2005 }}</ref>
*在纹理映射中GPU缓存一致性的Morton阶空间填充曲线,栅格化和湍流数据的索引
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*地震学<ref name="seismology" />
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*搜索和救援<ref name="search and rescue">{{cite journal| title=An Algorithmic Approach to Generate After-disaster Test Fields for Search and Rescue Agents| first1=Panteha |last1=Saeedi |first2=Soren A. |last2=Sorensen | journal=Proceedings of the World Congress on Engineering 2009 | year=2009 |pages=93–98 | isbn=978-988-17-0125-1|url=http://www.iaeng.org/publication/WCE2009/WCE2009_pp93-98.pdf}}</ref>
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*技术分析<ref>{{Cite book | last1=Bunde | first1=A.| last2=Havlin | first2=S.| chapter=Fractal Geometry, A Brief Introduction to | doi=10.1007/978-0-387-30440-3_218 | title=Encyclopedia of Complexity and Systems Science | pages=3700 | year=2009 | isbn=978-0-387-75888-6 }}</ref>
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*在纹理映射中GPU缓存一致性的Morton阶空间填充曲线<ref>{{cite web|title=GPU internals|url=http://fileadmin.cs.lth.se/cs/Personal/Michael_Doggett/pubs/doggett12-tc.pdf}}</ref><ref>{{cite web|title=sony patents|url=https://www.google.ch/patents/US20150287166?dq=morton+order+texture+swizzling}}</ref><ref>{{cite web|title = description of swizzled and hybrid tiled swizzled textures|url=https://news.ycombinator.com/item?id=2239173}}</ref> ,栅格化<ref>{{cite web | title=US8773422B1 - System, method, and computer program product for grouping linearly ordered primitives | website=Google Patents | date=December 4, 2007 | url=http://www.google.com/patents/US8773422 | access-date=December 28, 2019}}</ref><ref>{{cite web | title=US20110227921A1 - Processing of 3D computer graphics data on multiple shading engines | website=Google Patents | date=December 15, 2010 | url=http://www.google.ch/patents/US20110227921 | access-date=December 27, 2019}}</ref> 和湍流数据的索引<ref>{{cite web |url=http://turbulence.pha.jhu.edu |title=Johns Hopkins Turbulence Databases}}</ref><ref>{{cite journal|last=Li|first=Y.|first2=E.|last2=Perlman|first3=M.|last3=Wang|first4=y.|last4=Yang|first5=C.|last5=Meneveau|first6=R.|last6=Burns|first7=S.|last7=Chen|first8=A.|last8=Szalay|first9=G.|last9=Eyink|title=A Public Turbulence Database Cluster and Applications to Study Lagrangian Evolution of Velocity Increments in Turbulence|journal=Journal of Turbulence|date=2008|volume=9|pages=N31|doi=10.1080/14685240802376389|arxiv=0804.1703|bibcode=2008JTurb...9...31L}}</ref>。
 
下面对于分形几何在电子技术方面的应用做一些说明:
 
下面对于分形几何在电子技术方面的应用做一些说明:
 
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===分形天线===
 
===分形天线===
   −
分形天线是一种无线通信用的新概念天线。和传统天线相比,它在同样面积或体积的条件下具有最大的有效长度或周长。这种天线具有极端紧凑和多宽频带等特性,非常适合于RFID和移动通讯方面的应用。由于现代通信工具种类越来越多,体积也越来越小,因而需要把天线做得很小很小,而且越小越好。为此目的,把天线的形状做成分形是个好主意,因为这可以在同样面积的限制条件下把天线做得很长,而且还能取代多条天线而同时工作在几个不同频率区间之中。
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分形天线是一种无线通信用的新概念天线。和传统天线相比,它在同样面积或体积的条件下具有最大的有效长度或周长。这种天线具有极端紧凑和多宽频带等特性,非常适合于RFID和移动通讯方面的应用。由于现代通信工具种类越来越多,体积也越来越小,因而需要把天线做得很小很小,而且越小越好。为此目的,把天线的形状做成分形是个好主意,因为这可以在同样面积的限制条件下把天线做得很长,而且还能取代多条天线而同时工作在几个不同频率区间之中。<ref name="antenna">{{cite journal |last1=Hohlfeld |first1=Robert G. |last2=Cohen |first2=Nathan |title=Self-similarity and the geometric requirements for frequency independence in Antennae |journal=Fractals |volume=7 |issue=1 |pages=79–84 |year=1999 |doi=10.1142/S0218348X99000098 }}</ref>
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===离子推进===
 
===离子推进===
   −
当二维空间的分形被多次迭代时,分形的周长增加到无穷大,但面积绝不会超过某一阈值。 三维空间的分形与此相似,这样的分形可能有无限的表面积,但体积绝不会超过某一阈值。[111] 在选择电子发射体的结构和材料时,这样的特性可以用来最大限度地提高离子推进的效率。 如果操作正确,可使排放效率达到最高。[112]
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当二维空间的分形被多次迭代时,分形的周长增加到无穷大,但面积绝不会超过某一阈值。 三维空间的分形与此相似,这样的分形可能有无限的表面积,但体积绝不会超过某一阈值。<ref>{{Cite web|url=http://www.fractal.org/Bewustzijns-Besturings-Model/Fractals-Useful-Beauty.htm|title=Introduction to Fractal Geometry|website=www.fractal.org|access-date=2017-04-11}}</ref>在选择电子发射体的结构和材料时,这样的特性可以用来最大限度地提高离子推进的效率。 如果操作正确,可使排放效率达到最高。<ref>{{Cite news|url=https://www.nasa.gov/centers/glenn/about/fs21grc.html|title=NASA – Ion Propulsion|last=DeFelice|first=David|date=August 18, 2015|work=NASA|access-date=2017-04-11|language=en}}</ref>
    
==著名学者简介==
 
==著名学者简介==
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