1. Set Up a Scan

    2. Scan an Image

  2. View and Save the Results

      3. The results are displayed in the Results Table and in graphics, depending on the settings from Step 1. Several versions of the fractal dimension are provided. The columns listing the average and minimum cover Dʙs reflect the results for multiple origins. The smoothed Dʙ is found from smoothing horizontal intervals from the regression line by removing successive box sizes yielding the same number of boxes. See the User's Guide for more information.

NOTE:

  • Options include type of box size series as well as other scanning features that can affect the results for different types of images. For instance, a Relative Series is calculated relative to the largest box using exact factors; thus, setting the maximum box size to 48 generates the box sizes {1,2,3,4,6,8,12,16,24,48}, whereas setting it to 49 generates {1,7,49}. Refer to the current User's Guide (2006) for more information.
  • For multifractal analyses and sliding box lacunarity analyses, certain settings, in particular the minimum resolvable box size, may need special attention.
    • If the red and green parts of the MF graph of ƒ(α) do not meet in a continuous curve or if they appear to cross over, for instance, sampling may be inappropriate. To correct this, try using a scaled series, increasing the minimum grid size in pixels, or increasing the number of box sizes.
    • For sliding box lacunarity, it is important in some cases to keep the minimum resolvable size (i.e., minimum grid size in pixels)high enough (e.g.,usually greater than 3). In addition, using a nonexhaustive scan often yields the same basic results as an exhaustive scan for preliminary quick analyses. To use a nonexhaustive scan, keep the slide factors greater than one (e.g., 5); setting the x and y slide factors to 1 does an exhaustive scan.
    • Note that the number of box sizes can affect the result, especially in a multifractal analysis. To reduce processing time in both multifractal and lacunarity analyses, it is often helpful to use a relatively small number of box sizes. Do this by setting the number of different box sizes to 10 or 20, for instance.
    • For a random mass multifractal analysis, you may need to adjust the maximum percent to 100%, ensure the number of box sizes is not too high and not too low, and ensure the minimum grid size in pixels is high enough (e.g., >5 or 10).

      • References for FracLac

      To cite ImageJ, see the IJ site.
    • To cite FracLac use,

    In addition, below is a sample of citations in different disciplines where FracLac has been used.

    1. Agrawal AA. Plant defense and density dependence in the population growth of herbivores. Am Nat. July 2004; 164(1): 113-20.
    2. Agudera M, Banati R. Towards a molecular definition of activated microglia. 4th Biennial Research Conference: From Cell to Society. Sydney, Australia: University of Sydney, 2004.
    3. Agudera M, Robinson J, Banati R. Investigation of microglial activation with [3H] (R) PK11195 and CD-68 macrophage marker in human brain tumours. The Biennial Health Research Conference: From Cell to Society. Sydney, Australia: University of Sydney, 2006.
    4. Agui JH. Lunar dust characterization for exploration life support systems. 45th AIAA Aerospace Sciences Meeting and Exhibit. NASA Glenn Research Center, Cleveland, 2007.
    5. Amorim L, Filho, MB, Cruz, D. Analysing Recife's Urban Fragments. Proceedings of the 7th International Space Syntax Symposium. Eds. Daniel Koch, Lars Marcus, and Jesper Steen. Stockholm: KTH, 2009.
    6. Barto EK, Cipollini D. Garlic Mustard (Alliaria petiolata) Removal Method Affects Native Establishment. Invasive Plant Science and Management Jul 2009: 2(3): 230-236.
    7. Andjelkovic J, Zivic, N, Reljin B, Celebic V, Salom I. Application of Multifractal Analysis on Medical Images. WSEAS Transactions on Info Sci and Applications. November 2008; 11(5): 1561-1572.
    8. Buchman N, Cuddington K. Influences of Pea Morphology and Interacting Factors on Pea Aphid (Homoptera: Aphididae) Reproduction. Environmental Entomology. 38(4):962-970.
    9. Davila RE. Advances in Animal Blood Processing: Development of a Biopreserveration system and insights on the functional properties of plasma. University di Girona, Spain, 2006.
    10. Díaz JR, Payá JJM, Pérez LMM, Cortés M-ÁP, Andreo AM-A. Morphometric and architectonic study of proximal femur share. IX National Congress of Physical Therapy. Murcia, Spain: UCAM, San Antonio Catholic University of Murcia, 2006.
    11. Debergh I, Van Damme N, Pattyn P, Peeters M, Ceelen WP. The low-molecular-weight heparin, nadroparin, inhibits tumour angiogenesis in a rodent dorsal skinfold chamber model. Br J Cancer. March 2, 2010; 102(5): 837-43.
    12. De Gryze S, Jassogne L, Six J, Bossuyt H, Wevers M, Merckx R. Pore structure changes during decomposition of fresh residue: X-ray tomography analyses. Geoderma. September 2006; 134(1-2): 82-96.
    13. Dominkovics C, Harsanyi G. Fractal description of dendrite growth during electrochemical migration. Per. Pol. Elec. Eng.. 2008; 52(1-2): 13-19.
    14. Filho M. A morfologia da habitabilidade intra-urbana: o uso de imagem CBERS-2 na análise de padrões morfológicos no Recife. Anais XIII Simpósio Brasileiro de Sensoriamento Remoto. Florianópolis, Brasil. INPE, 2007; 769-776.
    15. Filho MB, Sobreira F. Accuracy of Lacunarity Algorithms in Texture Classification of High Spatial Resolution Images from Urban Areas. The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3b. 2008.
    16. Filho MB, Sobreira F. Assessing texture patterns in slums across scales: An unsupervised approach. CASA papers. London, UK: Centre for Advanced Spatial Analysis, University College, 2007.
    17. Fukushima A, Tomita, TsutomuImage Analyses of the Kinetic Changes of Conjunctival Hyperemia in Histamine-Induced Conjunctivitis in Guinea Pigs. Cornea. July 2009; 28(6): 694-698.
    18. Hamida T, Babadagli T. Effect Of Ultrasonic Waves On Immiscible And Miscible Displacement In Porous Media. SPE Annual Technical Conference and Exhibition, Dallas, Texas, October 2005.
    19. Jelinek H, Karperien A, Bossomaier T, Buchan A. Differentiating grades of microglia activation with fractal analysis. Proceedings of the 7th Asia-Pacific Conference on Complex Systems. Cairns, Australia, 2004; 605-612.
    20. Jelinek H, Karperien A, Cornforth D, Cesar R, Leandro G. MicroMod - an L-systems approach to neural modelling. Sixth Australia-Japan Joint Workshop on Intelligent and Evolutionary Systems. Canberra, Australia, 2002.
    21. Kam Y, Karperien A, Weidow B, Estrada L, Anderson A, Quaranta V. Nest expansion assay: a cancer systems biology approach to in vitro invasion measurements. BMC Reseach Notes. July 13, 2009; 2(130).
    22. Karperien A, Jelinek H, Bossomaier T. Overt and subtle effects of naloxone and lipopolysaccharide on cultured rat microglia. 7th Asia-Pacific Conference on Complex Systems. Cairns, Australia, 2004.
    23. Karperien A, Lucas A, Jelinek H. Fractal analysis of microglial morphology. Towards a science of complex systems. Paris, 2005.
    24. Lagarias A. Fractal analysis of the urbanization at the outskirts of the city: Models, measurement and explanation. Cybergeo: European Journal of Geography. July 16, 2007; Document 391.
    25. Lin KY, Maricevich M, Bardeesy N, Weissleder R, Mahmood U. In Vivo Quantitative Microvasculature Phenotype Imaging of Healthy and Malignant Tissues Using a Fiber-Optic Confocal Laser Microprobe1 Translational Oncology. July 2008; 1(2): 84-94.
    26. Mancardi D, Varetto G, Bucci E, Maniero F, Guiot C. Fractal parameters and vascular networks: facts & artifacts. Theoretical Biology and Medical Modelling. July 17, 2008; 5(12).
    27. Saeedi P, Sorensen S. An Algorithmic Approach to Generate After-disaster Test Fields for Search and Rescue Agents. Proceedings of the World Congress on Engineering. London, UK, 2009.
    28. Schulze MM, Hutchings N, Simpson TL. The Use of Fractal Analysis and Photometry to Estimate the Accuracy of Bulbar Redness Grading Scales. Investigative Ophthalmology & Visual Science. April 2008; 49(4): 1398-1406.
    29. Sener B. Lacunarity analysis of TEM Images. Innovations in Chemical Biology. Ed. Bilge Sener. Springer: 2008: Chapter 47.
    30. Shapland F, Baggott GK. The effect of static incubation on the yolk sac vasculature of the Japanese quail (Coturnix c. japonica). Avian and Poultry Biology Reviews. 2006; 17(2): 69.
    31. Sleutel S, Cnudde V, Masschaele B, Vlassenbroek J, Dierick M,Van Hoorebeke L, Jacobs P, De Neve S. Comparison of different nano- and micro-focus X-ray computed tomography set-ups for the visualization of the soil microstructure and soil organic matter. Computers & Geosciences. August 2008: 34(8): 931-938.
    32. Smajda R, Kukovecz Á, Kónya Z, Kiricsi I. Structure and gas permeability of multi-wall carbon nanotube buckypapers. Carbon. 2007; 45(6): 1176-1184.
    33. Tan S, Su A, Ford W. Aggregation of a hydrophobically modified poly(propylene imine) dendrimer. The European Physical Journal E: Soft Matter and Biological Physics. October 2008; 27(2): 205-211.
    34. Valous NA, Sun D-W, Allen P, Mendoza F. The use of lacunarity for visual texture characterization of pre-sliced cooked pork ham surface intensities Food Research International. January 2010; 43(1): 387-395.
    35. Vannucchi P, Leoni L. Structural characterization of the Costa Rica decollement: Evidence for seismically-induced fluid pulsing. Earth and Planetary Science Letters. 30 October 2007; 262(3-4): 413-428.
    36. Watson L, Vargas LM, Pineda L, Santaella E. Surface roughness and texture: Experiments and simulations. Ciencia E Ingeniería Neogranadina 2006; 16(2).
    37. Yasar F, Akgünlü F. Fractal dimension and lacunarity analysis of dental radiographs. Dentomaxillofac Radiol. 2005; 34: 261-267.