@article{ballDiffusioncontrolledAggregationContinuum1984,
  title = {Diffusion-Controlled Aggregation in the Continuum Approximation},
  author = {Ball, R. and Nauenberg, M. and Witten, T. A.},
  date = {1984-04-01},
  journaltitle = {Physical Review A},
  shortjournal = {Phys. Rev. A},
  volume = {29},
  number = {4},
  pages = {2017--2020},
  issn = {0556-2791},
  doi = {10.1103/PhysRevA.29.2017},
  url = {https://link.aps.org/doi/10.1103/PhysRevA.29.2017},
  urldate = {2023-03-15},
  langid = {english},
  file = {/Users/joshuacoles/Zotero/storage/DWGMBBIH/Ball et al. - 1984 - Diffusion-controlled aggregation in the continuum .pdf}
}

@article{battyUrbanGrowthForm1989,
  title = {Urban {{Growth}} and {{Form}}: {{Scaling}}, {{Fractal Geometry}}, and {{Diffusion-Limited Aggregation}}},
  shorttitle = {Urban {{Growth}} and {{Form}}},
  author = {Batty, M and Longley, P and Fotheringham, S},
  date = {1989-11},
  journaltitle = {Environment and Planning A: Economy and Space},
  shortjournal = {Environ Plan A},
  volume = {21},
  number = {11},
  pages = {1447--1472},
  issn = {0308-518X, 1472-3409},
  doi = {10.1068/a211447},
  url = {http://journals.sagepub.com/doi/10.1068/a211447},
  urldate = {2023-03-15},
  abstract = {In this paper, we propose a model of growth and form in which the processes of growth are intimately linked to the resulting geometry of the system. The model, first developed by Witten and Sander and referred to as the diffusion-limited aggregation or DLA model, generates highly ramified tree-like clusters of particles, or populations, with evident self-similarity about a fixed point. The extent to which such clusters fill space is measured by their fractal dimension which is estimated from scaling relationships linking population and density to distances within the cluster. We suggest that this model provides a suitable baseline for the development of models of urban structure and density which manifest similar scaling properties. A typical DLA simulation is presented and a variety of measures of its structure and dynamics are developed. These same measures are then applied to the urban growth and form of Taunton, a small market town in South West England, and important similarities and differences with the DLA simulation are discussed. We suggest there is much potential in extending analogies between DLA and urban form, and we also suggest future research directions involving variants of DLA and better measures of urban density.},
  langid = {english},
  file = {/Users/joshuacoles/Zotero/storage/F2M3CGET/batty1989.pdf.pdf;/Users/joshuacoles/Zotero/storage/YAGMYPYZ/Batty et al. - 1989 - Urban Growth and Form Scaling, Fractal Geometry, .pdf}
}

@article{bentleyMultidimensionalBinarySearch1975,
  title = {Multidimensional Binary Search Trees Used for Associative Searching},
  author = {Bentley, Jon Louis},
  date = {1975-09},
  journaltitle = {Communications of the ACM},
  shortjournal = {Commun. ACM},
  volume = {18},
  number = {9},
  pages = {509--517},
  issn = {0001-0782, 1557-7317},
  doi = {10.1145/361002.361007},
  url = {https://dl.acm.org/doi/10.1145/361002.361007},
  urldate = {2023-03-18},
  abstract = {This paper develops the multidimensional binary search tree (or               k               -d tree, where               k               is the dimensionality of the search space) as a data structure for storage of information to be retrieved by associative searches. The               k               -d tree is defined and examples are given. It is shown to be quite efficient in its storage requirements. A significant advantage of this structure is that a single data structure can handle many types of queries very efficiently. Various utility algorithms are developed; their proven average running times in an               n               record file are: insertion,               O               (log               n               ); deletion of the root,               O               (               n                                (                 k                 -1)/                 k                              ); deletion of a random node,               O               (log               n               ); and optimization (guarantees logarithmic performance of searches),               O               (               n               log               n               ). Search algorithms are given for partial match queries with               t               keys specified [proven maximum running time of               O               (               n                                (                 k                 -                 t                 )/                 k                              )] and for nearest neighbor queries [empirically observed average running time of               O               (log               n               ).] These performances far surpass the best currently known algorithms for these tasks. An algorithm is presented to handle any general intersection query. The main focus of this paper is theoretical. It is felt, however, that               k               -d trees could be quite useful in many applications, and examples of potential uses are given.},
  langid = {english},
  file = {/Users/joshuacoles/Zotero/storage/EZJWE76J/Bentley - 1975 - Multidimensional binary search trees used for asso.pdf}
}

@article{botetClusteringClustersProcesses1985,
  title = {Clustering of Clusters Processes above Their Upper Critical Dimensionalities},
  author = {Botet, R},
  date = {1985-04-01},
  journaltitle = {Journal of Physics A: Mathematical and General},
  shortjournal = {J. Phys. A: Math. Gen.},
  volume = {18},
  number = {5},
  pages = {847--855},
  issn = {0305-4470, 1361-6447},
  doi = {10.1088/0305-4470/18/5/017},
  url = {https://iopscience.iop.org/article/10.1088/0305-4470/18/5/017},
  urldate = {2023-02-24},
  file = {/Users/joshuacoles/Zotero/storage/CDI267Y4/botet1985.pdf.pdf}
}

@article{botetSizeDistributionClusters1984,
  title = {Size Distribution of Clusters in Irreversible Kinetic Aggregation},
  author = {Botet, R and Jullien, R},
  date = {1984-08-21},
  journaltitle = {Journal of Physics A: Mathematical and General},
  shortjournal = {J. Phys. A: Math. Gen.},
  volume = {17},
  number = {12},
  pages = {2517--2530},
  issn = {0305-4470, 1361-6447},
  doi = {10.1088/0305-4470/17/12/022},
  url = {https://iopscience.iop.org/article/10.1088/0305-4470/17/12/022},
  urldate = {2023-02-24},
  file = {/Users/joshuacoles/Zotero/storage/CV6NW42A/botet1984.pdf.pdf}
}

@book{lawlerIntersectionsRandomWalks2013,
  title = {Intersections of Random Walks},
  author = {Lawler, Gregory F.},
  date = {2013},
  series = {Modern {{Birkhäuser}} Classics},
  publisher = {{Birkhäuser}},
  location = {{New York}},
  isbn = {978-1-4614-5971-2 978-1-4614-5972-9},
  pagetotal = {223},
  keywords = {Random walks (Mathematics)},
  annotation = {OCLC: ocn812067146},
  file = {/Users/joshuacoles/Zotero/storage/C3TSALXD/Lawler - 2013 - Intersections of random walks.pdf}
}

@article{liStorageAddressingScheme2013,
  title = {Storage and Addressing Scheme for Practical Hexagonal Image Processing},
  author = {Li, Xiangguo},
  date = {2013-01-31},
  journaltitle = {Journal of Electronic Imaging},
  shortjournal = {J. Electron. Imaging},
  volume = {22},
  number = {1},
  pages = {010502},
  issn = {1017-9909},
  doi = {10.1117/1.JEI.22.1.010502},
  url = {http://electronicimaging.spiedigitallibrary.org/article.aspx?doi=10.1117/1.JEI.22.1.010502},
  urldate = {2023-03-04},
  langid = {english}
}

@article{lyonsSimpleCriterionTransience1983,
  title = {A {{Simple Criterion}} for {{Transience}} of a {{Reversible Markov Chain}}},
  author = {Lyons, Terry},
  date = {1983-05-01},
  journaltitle = {The Annals of Probability},
  shortjournal = {Ann. Probab.},
  volume = {11},
  number = {2},
  issn = {0091-1798},
  doi = {10.1214/aop/1176993604},
  url = {https://projecteuclid.org/journals/annals-of-probability/volume-11/issue-2/A-Simple-Criterion-for-Transience-of-a-Reversible-Markov-Chain/10.1214/aop/1176993604.full},
  urldate = {2023-03-13},
  file = {/Users/joshuacoles/Zotero/storage/65P85MN4/Lyons - 1983 - A Simple Criterion for Transience of a Reversible .pdf}
}

@article{nicolas-carlockUniversalDimensionalityFunction2019,
  title = {A Universal Dimensionality Function for the Fractal Dimensions of {{Laplacian}} Growth},
  author = {Nicolás-Carlock, J. R. and Carrillo-Estrada, J. L.},
  date = {2019-02-04},
  journaltitle = {Scientific Reports},
  shortjournal = {Sci Rep},
  volume = {9},
  number = {1},
  pages = {1120},
  issn = {2045-2322},
  doi = {10.1038/s41598-018-38084-3},
  url = {https://www.nature.com/articles/s41598-018-38084-3},
  urldate = {2023-03-15},
  abstract = {Abstract             Laplacian growth, associated to the diffusion-limited aggregation (DLA) model or the more general dielectric-breakdown model (DBM), is a fundamental out-of-equilibrium process that generates structures with characteristic fractal/non-fractal morphologies. However, despite diverse numerical and theoretical attempts, a data-consistent description of the fractal dimensions of the mass-distributions of these structures has been missing. Here, an analytical model of the fractal dimensions of the DBM and DLA is provided by means of a recently introduced dimensionality equation for the scaling of clusters undergoing a continuous morphological transition. Particularly, this equation relies on an effective information-function dependent on the Euclidean dimension of the embedding-space and the control parameter of the system. Numerical and theoretical approaches are used in order to determine this information-function for both DLA and DBM. In the latter, a connection to the Rényi entropies and generalized dimensions of the cluster is made, showing that DLA could be considered as the point of maximum information-entropy production along the DBM transition. The results are in good agreement with previous theoretical and numerical estimates for two- and three-dimensional DBM, and high-dimensional DLA. Notably, the DBM dimensions conform to a universal description independently of the initial cluster-configuration and the embedding-space.},
  langid = {english},
  file = {/Users/joshuacoles/Zotero/storage/TLE4AFWZ/10.1038@s41598-018-38084-3.pdf.pdf;/Users/joshuacoles/Zotero/storage/ZJDV8CJF/Nicolás-Carlock and Carrillo-Estrada - 2019 - A universal dimensionality function for the fracta.pdf}
}

@article{niemeyerFractalDimensionDielectric1984,
  title = {Fractal {{Dimension}} of {{Dielectric Breakdown}}},
  author = {Niemeyer, L. and Pietronero, L. and Wiesmann, H. J.},
  date = {1984-03-19},
  journaltitle = {Physical Review Letters},
  shortjournal = {Phys. Rev. Lett.},
  volume = {52},
  number = {12},
  pages = {1033--1036},
  issn = {0031-9007},
  doi = {10.1103/PhysRevLett.52.1033},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.52.1033},
  urldate = {2023-03-02},
  langid = {english},
  file = {/Users/joshuacoles/Zotero/storage/LKJWGEMV/niemeyer1984.pdf.pdf}
}

@article{procacciaDimensionDiffusionlimitedAggregates2021,
  title = {Dimension of Diffusion-Limited Aggregates Grown on a Line},
  author = {Procaccia, Eviatar B. and Procaccia, Itamar},
  date = {2021-02-09},
  journaltitle = {Physical Review E},
  shortjournal = {Phys. Rev. E},
  volume = {103},
  number = {2},
  pages = {L020101},
  issn = {2470-0045, 2470-0053},
  doi = {10.1103/PhysRevE.103.L020101},
  url = {https://link.aps.org/doi/10.1103/PhysRevE.103.L020101},
  urldate = {2023-03-15},
  langid = {english},
  file = {/Users/joshuacoles/Zotero/storage/BA59EJ99/Procaccia and Procaccia - 2021 - Dimension of diffusion-limited aggregates grown on.pdf}
}

@article{sanderDiffusionlimitedAggregationKinetic2000,
  title = {Diffusion-Limited Aggregation: {{A}} Kinetic Critical Phenomenon?},
  shorttitle = {Diffusion-Limited Aggregation},
  author = {Sander, Leonard M.},
  date = {2000-07},
  journaltitle = {Contemporary Physics},
  shortjournal = {Contemporary Physics},
  volume = {41},
  number = {4},
  pages = {203--218},
  issn = {0010-7514, 1366-5812},
  doi = {10.1080/001075100409698},
  url = {http://www.tandfonline.com/doi/abs/10.1080/001075100409698},
  urldate = {2023-03-02},
  langid = {english},
  file = {/Users/joshuacoles/Zotero/storage/YV9XD9VR/sander2000.pdf.pdf}
}

@article{smithFractalMethodsResults1996a,
  title = {Fractal Methods and Results in Cellular Morphology — Dimensions, Lacunarity and Multifractals},
  author = {Smith, T.G. and Lange, G.D. and Marks, W.B.},
  date = {1996-11},
  journaltitle = {Journal of Neuroscience Methods},
  shortjournal = {Journal of Neuroscience Methods},
  volume = {69},
  number = {2},
  pages = {123--136},
  issn = {01650270},
  doi = {10.1016/S0165-0270(96)00080-5},
  url = {https://linkinghub.elsevier.com/retrieve/pii/S0165027096000805},
  urldate = {2023-03-16},
  langid = {english},
  file = {/Users/joshuacoles/Zotero/storage/ZWIYRKBT/Smith et al. - 1996 - Fractal methods and results in cellular morphology.pdf}
}

@article{tanInfluenceExternalField2000,
  title = {Influence of External Field on Diffusion-Limited Aggregation},
  author = {Tan, Zhi-Jie and Zou, Xian-Wu and Zhang, Wen-Bing and Jin, Zhun-Zhi},
  date = {2000-04},
  journaltitle = {Physics Letters A},
  shortjournal = {Physics Letters A},
  volume = {268},
  number = {1-2},
  pages = {112--116},
  issn = {03759601},
  doi = {10.1016/S0375-9601(00)00143-2},
  url = {https://linkinghub.elsevier.com/retrieve/pii/S0375960100001432},
  urldate = {2023-03-15},
  abstract = {The influence of external electric field on diffusion-limited aggregation ŽDLA. has been investigated by computer simulations. When the parameter l increases from 0 to `, the morphology of aggregates changes from pure DLA to chain-like pattern gradually, where l stands for the relative strength of field-induced dipolar interaction to thermal energy. The structure transition is the transition between a prototype disorder structure and a relative order one in essence. The reason of the transition is the interaction controlling systems changes from thermal force to field-induced dipolar interactions with l rising. q 2000 Elsevier Science B.V. All rights reserved.},
  langid = {english},
  file = {/Users/joshuacoles/Zotero/storage/34TKRN2A/Tan et al. - 2000 - Influence of external field on diffusion-limited a.pdf}
}

@article{tentiFractalDimensionDiffusionlimited2021,
  title = {Fractal Dimension of Diffusion-Limited Aggregation Clusters Grown on Spherical Surfaces},
  author = {Tenti, J. M. and Hernández Guiance, S. N. and Irurzun, I. M.},
  date = {2021-01-29},
  journaltitle = {Physical Review E},
  shortjournal = {Phys. Rev. E},
  volume = {103},
  number = {1},
  pages = {012138},
  issn = {2470-0045, 2470-0053},
  doi = {10.1103/PhysRevE.103.012138},
  url = {https://link.aps.org/doi/10.1103/PhysRevE.103.012138},
  urldate = {2023-03-15},
  langid = {english},
  file = {/Users/joshuacoles/Zotero/storage/G4IEQGY6/tenti2021.pdf.pdf}
}

@article{tokuyamaFractalDimensionsDiffusionlimited1984,
  title = {Fractal Dimensions for Diffusion-Limited Aggregation},
  author = {Tokuyama, M. and Kawasaki, K.},
  date = {1984-02},
  journaltitle = {Physics Letters A},
  shortjournal = {Physics Letters A},
  volume = {100},
  number = {7},
  pages = {337--340},
  issn = {03759601},
  doi = {10.1016/0375-9601(84)91083-1},
  url = {https://linkinghub.elsevier.com/retrieve/pii/0375960184910831},
  urldate = {2023-03-15},
  langid = {english},
  file = {/Users/joshuacoles/Zotero/storage/9XURJU5X/tokuyama1984.pdf.pdf;/Users/joshuacoles/Zotero/storage/JGBE6A2Y/Tokuyama and Kawasaki - 1984 - Fractal dimensions for diffusion-limited aggregati.pdf}
}

@article{turkevichProbabilityScalingDiffusionlimited1986,
  title = {Probability Scaling for Diffusion-Limited Aggregation in Higher Dimensions},
  author = {Turkevich, Leonid A. and Scher, Harvey},
  date = {1986-01-01},
  journaltitle = {Physical Review A},
  shortjournal = {Phys. Rev. A},
  volume = {33},
  number = {1},
  pages = {786--788},
  issn = {0556-2791},
  doi = {10.1103/PhysRevA.33.786},
  url = {https://link.aps.org/doi/10.1103/PhysRevA.33.786},
  urldate = {2023-03-15},
  langid = {english},
  file = {/Users/joshuacoles/Zotero/storage/FSHPX9RK/turkevich1986.pdf.pdf}
}

@book{vicsekFractalGrowthPhenomena1992,
  title = {Fractal Growth Phenomena},
  author = {Vicsek, Tamás},
  date = {1992},
  edition = {2nd ed},
  publisher = {{World Scientific}},
  location = {{Singapore ; New Jersey}},
  isbn = {978-981-02-0668-0 978-981-02-0669-7},
  langid = {english},
  pagetotal = {488},
  keywords = {Fractals},
  note = {Semi-vetted, source Aengus},
  file = {/Users/joshuacoles/Zotero/storage/LJP5C4WG/Vicsek - 1992 - Fractal growth phenomena.pdf}
}

@article{wittenDiffusionlimitedAggregation1983,
  title = {Diffusion-Limited Aggregation},
  author = {Witten, T. A. and Sander, L. M.},
  date = {1983-05-01},
  journaltitle = {Physical Review B},
  shortjournal = {Phys. Rev. B},
  volume = {27},
  number = {9},
  pages = {5686--5697},
  issn = {0163-1829},
  doi = {10.1103/PhysRevB.27.5686},
  url = {https://link.aps.org/doi/10.1103/PhysRevB.27.5686},
  urldate = {2023-02-24},
  langid = {english},
  note = {Unvetted, source google},
  file = {/Users/joshuacoles/Zotero/storage/ZP38RVBK/ZP38RVBK.pdf}
}

@article{wuDependenceFractalDimension2013,
  title = {Dependence of Fractal Dimension of {{DLCA}} Clusters on Size of Primary Particles},
  author = {Wu, Hua and Lattuada, Marco and Morbidelli, Massimo},
  date = {2013-07},
  journaltitle = {Advances in Colloid and Interface Science},
  shortjournal = {Advances in Colloid and Interface Science},
  volume = {195--196},
  pages = {41--49},
  issn = {00018686},
  doi = {10.1016/j.cis.2013.04.001},
  url = {https://linkinghub.elsevier.com/retrieve/pii/S0001868613000353},
  urldate = {2023-03-15},
  langid = {english},
  file = {/Users/joshuacoles/Zotero/storage/KMWTNPKN/wu2013.pdf.pdf}
}
