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Volumn 84, Issue 11, 2006, Pages 1675-1685

Stochastic approaches in phyllotaxis

Author keywords

Development; Entropy; Mutants; Order; Patterns; Phyllotaxis

Indexed keywords

CELL CULTURE; ENTROPY; PROBABILITY; STATISTICAL METHODS;

EID: 34248374834     PISSN: 00084026     EISSN: None     Source Type: Journal    
DOI: 10.1139/B06-116     Document Type: Short Survey
Times cited : (6)

References (118)
  • 1
    • 0016165351 scopus 로고
    • A model of contact pressure in phyllotaxis
    • doi:10.1016/0022-5193(74)90043-5
    • Adler, I. 1974. A model of contact pressure in phyllotaxis. J. Theor. Biol. 45: 1-79. doi:10.1016/0022-5193(74)90043-5.
    • (1974) J. Theor. Biol , vol.45 , pp. 1-79
    • Adler, I.1
  • 2
    • 0010076855 scopus 로고    scopus 로고
    • The role of continued fractions in phyllotaxis
    • doi:10.1006/jabr.1997.7272
    • Adler, I. 1998. The role of continued fractions in phyllotaxis. J. Algebra, 205: 227-243. doi:10.1006/jabr.1997.7272.
    • (1998) J. Algebra , vol.205 , pp. 227-243
    • Adler, I.1
  • 3
    • 0030867693 scopus 로고    scopus 로고
    • A history of the study of phyllotaxis
    • Adler, I., Barabé, D., and Jean, R.V. 1997. A history of the study of phyllotaxis. Ann. Bot. (Lond.), 80: 231-244.
    • (1997) Ann. Bot. (Lond.) , vol.80 , pp. 231-244
    • Adler, I.1    Barabé, D.2    Jean, R.V.3
  • 4
    • 0037400084 scopus 로고    scopus 로고
    • Functional morphology and evolution of stem succulence in cacti
    • doi:10.1006/jare.2002.1059
    • Altesor, A., and Ezcurra, E. 2003. Functional morphology and evolution of stem succulence in cacti. J. Arid Environ. 53: 557-567. doi:10.1006/jare.2002.1059.
    • (2003) J. Arid Environ , vol.53 , pp. 557-567
    • Altesor, A.1    Ezcurra, E.2
  • 5
    • 0041346103 scopus 로고    scopus 로고
    • A dynamical system for plant pattern formation: A rigourous analysis
    • doi:10.1007/s00332-002-0513-1
    • Atela, P., Gole, C., and Hotton, S. 2002. A dynamical system for plant pattern formation: a rigourous analysis. J. Nonlinear Sci. 12: 641-676. doi:10.1007/s00332-002-0513-1.
    • (2002) J. Nonlinear Sci , vol.12 , pp. 641-676
    • Atela, P.1    Gole, C.2    Hotton, S.3
  • 8
    • 0343991632 scopus 로고
    • Chaos in plant morphology
    • Barabé, D. 1991. Chaos in plant morphology. Acta Biotheor. 39: 5-8.
    • (1991) Acta Biotheor , vol.39 , pp. 5-8
    • Barabé, D.1
  • 9
    • 1842712667 scopus 로고    scopus 로고
    • The use of entropy to analyse phyllotactic mutants: A theoretical analysis
    • doi:10.1105/tpc.160440
    • Barabé, D., and Jeune, B. 2004. The use of entropy to analyse phyllotactic mutants: a theoretical analysis. Plant Cell, 16: 804-806. doi:10.1105/tpc.160440.
    • (2004) Plant Cell , vol.16 , pp. 804-806
    • Barabé, D.1    Jeune, B.2
  • 10
    • 33745783120 scopus 로고    scopus 로고
    • Complexity and information in regular and random phyllotactic patterns
    • Barabé, D., and Jeune, B. 2006. Complexity and information in regular and random phyllotactic patterns. Riv. Biol. Biol. Forum, 99: 85-102.
    • (2006) Riv. Biol. Biol. Forum , vol.99 , pp. 85-102
    • Barabé, D.1    Jeune, B.2
  • 11
    • 0039968171 scopus 로고    scopus 로고
    • Phyllotactic order induced by symmetry breaking in advected Turings patterns
    • doi:10.1016/S0375-9601(97)00361-7
    • Bernasconi, G.P., and Boissonade, J. 1997. Phyllotactic order induced by symmetry breaking in advected Turings patterns. Phys. Lett. A, 232: 224-230. doi:10.1016/S0375-9601(97)00361-7.
    • (1997) Phys. Lett. A , vol.232 , pp. 224-230
    • Bernasconi, G.P.1    Boissonade, J.2
  • 12
    • 33749492272 scopus 로고    scopus 로고
    • Integrable discrete dynamics and Fibonacci sequences
    • Blackmore, D., and Kappraff, J. 1996. Integrable discrete dynamics and Fibonacci sequences. Zeit. Angew. Math. Mech. 76: Suppl.2, 49-52.
    • (1996) Zeit. Angew. Math. Mech , vol.76 , Issue.SUPPL.2 , pp. 49-52
    • Blackmore, D.1    Kappraff, J.2
  • 13
    • 4344559665 scopus 로고    scopus 로고
    • Number patterns in nature
    • doi:10.1016/j.cryseng.2003.11.004
    • Boeyens, J.C.A. 2003. Number patterns in nature. Cryst. Eng. 6: 167-185. doi:10.1016/j.cryseng.2003.11.004.
    • (2003) Cryst. Eng , vol.6 , pp. 167-185
    • Boeyens, J.C.A.1
  • 14
    • 0037738567 scopus 로고    scopus 로고
    • HASTY, the Arabidopsis ortholog of exportin 5/MSN5, regulates phase change and morphogenesis
    • doi:10.1242/dev.00362
    • Bollman, K.M., Aukerman, M.J., Park, M.Y., Hunter, C., Berardini, T.Z., and Poething, R.S. 2003. HASTY, the Arabidopsis ortholog of exportin 5/MSN5, regulates phase change and morphogenesis. Development, 130: 1493-1504. doi:10.1242/dev.00362.
    • (2003) Development , vol.130 , pp. 1493-1504
    • Bollman, K.M.1    Aukerman, M.J.2    Park, M.Y.3    Hunter, C.4    Berardini, T.Z.5    Poething, R.S.6
  • 16
  • 17
    • 0034182964 scopus 로고    scopus 로고
    • Conformities of spiral phyllotaxis
    • Bryntsev, V.A. 2000. Conformities of spiral phyllotaxis. Zh. Obshch. Biol. 61: 325-335.
    • (2000) Zh. Obshch. Biol , vol.61 , pp. 325-335
    • Bryntsev, V.A.1
  • 18
    • 0026023209 scopus 로고
    • Complex patterns formed by motile cells of Escherichia coli
    • doi:10.1038/349630a0
    • Budrene, E.O., and Berg, H.C. 1991. Complex patterns formed by motile cells of Escherichia coli. Nature, 349: 630-633. doi:10.1038/349630a0.
    • (1991) Nature , vol.349 , pp. 630-633
    • Budrene, E.O.1    Berg, H.C.2
  • 19
    • 0028100256 scopus 로고
    • Organ positions and pattern formation in the shoot
    • doi:10.1046/j.1365-313X.1994. 6010001.x
    • Callos, J.D., and Medford, J.I. 1994. Organ positions and pattern formation in the shoot. Plant J. 6: 1-7. doi:10.1046/j.1365-313X.1994. 6010001.x.
    • (1994) Plant J , vol.6 , pp. 1-7
    • Callos, J.D.1    Medford, J.I.2
  • 20
    • 0028676166 scopus 로고
    • The forever young gene encodes an oxidoreductase required for proper development of the Arabidopsis vegetative shoot apex
    • doi:10.1046/j.1365-313X.1994.6060835.x
    • Callos, J.D., DiRado, M., Xu, B., Behringer, F.J., Link, B.M., and Medford, J.I. 1994. The forever young gene encodes an oxidoreductase required for proper development of the Arabidopsis vegetative shoot apex. Plant J. 6: 835-847. doi:10.1046/j.1365-313X.1994.6060835.x.
    • (1994) Plant J , vol.6 , pp. 835-847
    • Callos, J.D.1    DiRado, M.2    Xu, B.3    Behringer, F.J.4    Link, B.M.5    Medford, J.I.6
  • 21
    • 0029556729 scopus 로고
    • Control of flower development and phyllotaxy by meristem identity genes in Anturrhinum
    • doi:10.1105/tpc.7.12.2001
    • Carpenter, R., Copsey, L., Vincent, C., Doyle, S., Magrath, R., and Coen, E. 1995. Control of flower development and phyllotaxy by meristem identity genes in Anturrhinum. Plant Cell, 7: 2001-2011. doi:10.1105/tpc.7.12.2001.
    • (1995) Plant Cell , vol.7 , pp. 2001-2011
    • Carpenter, R.1    Copsey, L.2    Vincent, C.3    Doyle, S.4    Magrath, R.5    Coen, E.6
  • 22
    • 84918358658 scopus 로고    scopus 로고
    • Chaitin, G.J. 1966. On the length of programs for computing finite binary sequences. J. Assoc. Comp. Mach. 13: 547-569.
    • Chaitin, G.J. 1966. On the length of programs for computing finite binary sequences. J. Assoc. Comp. Mach. 13: 547-569.
  • 23
    • 0003781307 scopus 로고
    • Information randomness & incompleteness
    • Papers on algorithmic Information Theory, World Scientific, Singapore
    • Chaitin, G.J. 1987. Information randomness & incompleteness. Papers on algorithmic Information Theory. Series in Computer Science. Vol. 8. World Scientific, Singapore.
    • (1987) Series in Computer Science , vol.8
    • Chaitin, G.J.1
  • 24
    • 0027131151 scopus 로고
    • Amp1 - a mutant with high cytokinin levels and altered embryonic pattern, faster vegetative growth, constitutive photomorphogenesis and precocious flowering
    • doi:10.1046/j.1365-313X.1993.04060907.x
    • Chaudhury, A.M., Letham, S., Craig, S., and Dennis, E.S. 1993. Amp1 - a mutant with high cytokinin levels and altered embryonic pattern, faster vegetative growth, constitutive photomorphogenesis and precocious flowering. Plant J. 4: 907-916. doi:10.1046/j.1365-313X.1993.04060907.x.
    • (1993) Plant J , vol.4 , pp. 907-916
    • Chaudhury, A.M.1    Letham, S.2    Craig, S.3    Dennis, E.S.4
  • 25
    • 0028887377 scopus 로고
    • CLAVATA3 is a regulator of shoot and floral meristem development affecting the same processes as CLAVATA1
    • Clark, S.E., Running, M.P., and Meyerowitz, E.M. 1993. CLAVATA3 is a regulator of shoot and floral meristem development affecting the same processes as CLAVATA1. Development, 121: 2057-2067.
    • (1993) Development , vol.121 , pp. 2057-2067
    • Clark, S.E.1    Running, M.P.2    Meyerowitz, E.M.3
  • 26
    • 33645011194 scopus 로고    scopus 로고
    • Do Fibonacci numbers reveal the involvement of geometrical imperatives or biological interactions in phyllotaxis?
    • doi:10.1111/j.1095-8339.2006.00490.x
    • Cooke, T.J. 2006. Do Fibonacci numbers reveal the involvement of geometrical imperatives or biological interactions in phyllotaxis? Bot. J. Linn. Soc. 150: 3-4. doi:10.1111/j.1095-8339.2006.00490.x.
    • (2006) Bot. J. Linn. Soc , vol.150 , pp. 3-4
    • Cooke, T.J.1
  • 27
    • 0346836011 scopus 로고    scopus 로고
    • Initial transitions, order and disorder in phyllotactic patterns: The ontogeny of Helianthus annuus. A case study
    • Couder, Y. 1998. Initial transitions, order and disorder in phyllotactic patterns: the ontogeny of Helianthus annuus. A case study. Acta Soc. Bot. Pol. 67: 129-150.
    • (1998) Acta Soc. Bot. Pol , vol.67 , pp. 129-150
    • Couder, Y.1
  • 28
    • 0032555060 scopus 로고    scopus 로고
    • A model of phyllotaxis
    • doi:10.1006/jtbi.1998.0682
    • Cummings, F.W., and Strickland, J.C. 1998. A model of phyllotaxis. J. Theor. Biol. 192: 531-544. doi:10.1006/jtbi.1998.0682.
    • (1998) J. Theor. Biol , vol.192 , pp. 531-544
    • Cummings, F.W.1    Strickland, J.C.2
  • 29
    • 0000778263 scopus 로고
    • Phyllotaxis as a physical self-organized process
    • Douady, S., and Couder, Y. 1992. Phyllotaxis as a physical self-organized process. Phys. Rev. Lett. 68: 2098-2101.
    • (1992) Phys. Rev. Lett , vol.68 , pp. 2098-2101
    • Douady, S.1    Couder, Y.2
  • 30
    • 0034975620 scopus 로고    scopus 로고
    • The developmental basis of floral variation in Drymis winteri (Winteraceae)
    • doi:10.1086/320790
    • Doust, A.N. 2001. The developmental basis of floral variation in Drymis winteri (Winteraceae). Int. J. Plant. Sci. 162: 697-717. doi:10.1086/320790.
    • (2001) Int. J. Plant. Sci , vol.162 , pp. 697-717
    • Doust, A.N.1
  • 31
    • 85010392744 scopus 로고
    • Chaotic floral phyllotaxis and reduced perianth in Achlys (Berberidaceae)
    • Endress, P. 1989. Chaotic floral phyllotaxis and reduced perianth in Achlys (Berberidaceae). Bot. Acta, 102: 159-163.
    • (1989) Bot. Acta , vol.102 , pp. 159-163
    • Endress, P.1
  • 32
    • 0037102206 scopus 로고    scopus 로고
    • Plant mathematics and Fibonacci's flowers
    • doi:10.1038/418723a
    • Fleming, A.J. 2002. Plant mathematics and Fibonacci's flowers. Nature, 418: 723. doi:10.1038/418723a.
    • (2002) Nature , vol.418 , pp. 723
    • Fleming, A.J.1
  • 33
    • 11844301381 scopus 로고    scopus 로고
    • Formation of primordia and phyllotaxy
    • doi:10.1016/j.pbi.2004.11.013
    • Fleming, A.J. 2005. Formation of primordia and phyllotaxy. Curr. Opin. Plant Biol. 8: 53-58. doi:10.1016/j.pbi.2004.11.013.
    • (2005) Curr. Opin. Plant Biol , vol.8 , pp. 53-58
    • Fleming, A.J.1
  • 34
    • 0033303553 scopus 로고    scopus 로고
    • Un possible lien entre la croissance dendritique en physique et la morphogenèse des plantes
    • Fleury, V. 1999. Un possible lien entre la croissance dendritique en physique et la morphogenèse des plantes. C.R. Acad. Sci. Ser. III Sci. Vie, 322: 725-734.
    • (1999) C.R. Acad. Sci. Ser. III Sci. Vie , vol.322 , pp. 725-734
    • Fleury, V.1
  • 36
    • 0042009555 scopus 로고    scopus 로고
    • Association of the Fibonacci Cascade with the distribution of coronary artery lesions responsible for ST-segment elevation myocardial infarction
    • doi:10.1016/S0002-9149(03)00731- 8
    • Gibson, C.M., Gibson, W.J., Murphy, S.A., Marble, S.J., McCabe, C.H., Turakhia, M.P., Kirtane, A.J., Karha, J., Aroesty, J.M., Giugliano, R.P., and Antman, E.M. 2003. Association of the Fibonacci Cascade with the distribution of coronary artery lesions responsible for ST-segment elevation myocardial infarction. Am. J. Cardiol. 92: 595-597. doi:10.1016/S0002-9149(03)00731- 8.
    • (2003) Am. J. Cardiol , vol.92 , pp. 595-597
    • Gibson, C.M.1    Gibson, W.J.2    Murphy, S.A.3    Marble, S.J.4    McCabe, C.H.5    Turakhia, M.P.6    Kirtane, A.J.7    Karha, J.8    Aroesty, J.M.9    Giugliano, R.P.10    Antman, E.M.11
  • 37
    • 0026171653 scopus 로고
    • Eigenshape analysis of a cut-grow mapping for triangles, and its application to phyllotaxis in plants
    • doi:10.1137/0151039
    • Goodall, C. 1991. Eigenshape analysis of a cut-grow mapping for triangles, and its application to phyllotaxis in plants. SIAM J. Appl. Math. 51: 775-798. doi:10.1137/0151039.
    • (1991) SIAM J. Appl. Math , vol.51 , pp. 775-798
    • Goodall, C.1
  • 38
    • 0033302353 scopus 로고    scopus 로고
    • Expression of patterns in plants: Combining molecular and calculus-based biophysical paradigms
    • doi:10.2307/2656967
    • Green, P.B. 1999. Expression of patterns in plants: combining molecular and calculus-based biophysical paradigms. Am. J. Bot. 86: 1059-1076. doi:10.2307/2656967.
    • (1999) Am. J. Bot , vol.86 , pp. 1059-1076
    • Green, P.B.1
  • 39
    • 0346271791 scopus 로고    scopus 로고
    • Attractive or repulsive interactions in different structure types
    • Hauk, J., and Mika, K. 2003. Attractive or repulsive interactions in different structure types. Prog. Solid State Chem. 31: 149-218.
    • (2003) Prog. Solid State Chem , vol.31 , pp. 149-218
    • Hauk, J.1    Mika, K.2
  • 40
    • 27644549049 scopus 로고    scopus 로고
    • Pattern of auxin transport and gene expression during primordium development revealed by live imaging of the Arabidopsis inflorescence meristem
    • doi:10.1016/j.cub. 2005.09.052
    • Heisler, M.G., Ohno, C., Das, P., Sieber, P., Reddy, G.V., Long, J.A., and Meyerowitz, E.M. 2005. Pattern of auxin transport and gene expression during primordium development revealed by live imaging of the Arabidopsis inflorescence meristem. Curr. Biol. 15: 1899-1911. doi:10.1016/j.cub. 2005.09.052.
    • (2005) Curr. Biol , vol.15 , pp. 1899-1911
    • Heisler, M.G.1    Ohno, C.2    Das, P.3    Sieber, P.4    Reddy, G.V.5    Long, J.A.6    Meyerowitz, E.M.7
  • 41
    • 3042959690 scopus 로고
    • On a probabilistic analogue of the Fibonacci sequence
    • doi:10.2307/3213217
    • Heyde, C.C. 1980. On a probabilistic analogue of the Fibonacci sequence. J. Appl. Prob. 17: 1079-1082. doi:10.2307/3213217.
    • (1980) J. Appl. Prob , vol.17 , pp. 1079-1082
    • Heyde, C.C.1
  • 42
    • 3042988886 scopus 로고
    • On Fibonacci (or lagged Bienaymé-Galton-Watson) branching processes
    • doi:10.2307/3213313
    • Heyde, C.C. 1981. On Fibonacci (or lagged Bienaymé-Galton-Watson) branching processes. J. Appl. Prob. 18: 583-591. doi:10.2307/3213313.
    • (1981) J. Appl. Prob , vol.18 , pp. 583-591
    • Heyde, C.C.1
  • 43
    • 0034525264 scopus 로고    scopus 로고
    • SHOOT ORGANIZATION genes regulate shoot apical meristem organization and the pattern of leaf primordium initiation in rice
    • doi:10.1105/tpc.12.11.2161
    • Itoh, J.-I., Kitano, H., Matsuoka, M., and Nagato, Y. 2000. SHOOT ORGANIZATION genes regulate shoot apical meristem organization and the pattern of leaf primordium initiation in rice. Plant Cell, 12: 2161-2174. doi:10.1105/tpc.12.11.2161.
    • (2000) Plant Cell , vol.12 , pp. 2161-2174
    • Itoh, J.-I.1    Kitano, H.2    Matsuoka, M.3    Nagato, Y.4
  • 44
    • 0032957303 scopus 로고    scopus 로고
    • Control of phyllotaxis in maize by the abphyl1 gene
    • Jackson, D., and Hake, S. 1999. Control of phyllotaxis in maize by the abphyl1 gene. Development, 126: 315-323.
    • (1999) Development , vol.126 , pp. 315-323
    • Jackson, D.1    Hake, S.2
  • 45
    • 34248343643 scopus 로고    scopus 로고
    • Jean, R.V. 1976. La G-entropie en phyllotaxie. Rev. Biol. Math. 55: 111-130.
    • Jean, R.V. 1976. La G-entropie en phyllotaxie. Rev. Biol. Math. 55: 111-130.
  • 46
    • 0018604535 scopus 로고
    • Some consequences of the hierarchical approach to phyllotaxis
    • doi:10.1016/0022-5193(79)90168- 1
    • Jean, R.V. 1979. Some consequences of the hierarchical approach to phyllotaxis. J. Theor. Biol. 81: 309-326. doi:10.1016/0022-5193(79)90168- 1.
    • (1979) J. Theor. Biol , vol.81 , pp. 309-326
    • Jean, R.V.1
  • 47
    • 0342485070 scopus 로고
    • A systemic model of growth in botanometry
    • doi:10.1016/0022-5193(80)90236-2
    • Jean, R.V. 1980. A systemic model of growth in botanometry. J. Theor. Biol. 87: 569-584. doi:10.1016/0022-5193(80)90236-2.
    • (1980) J. Theor. Biol , vol.87 , pp. 569-584
    • Jean, R.V.1
  • 48
    • 34248394914 scopus 로고    scopus 로고
    • Jean, R.V. (Editor). 1986. Théorème central et développements récents dans l'étude des patterns observés chez les plantes. In Biomathématique. Cahiers de l'ACFAS No. 45. Association canadienne-française pour l'avancement des sciences, Québec. pp. 79-88.
    • Jean, R.V. (Editor). 1986. Théorème central et développements récents dans l'étude des patterns observés chez les plantes. In Biomathématique. Cahiers de l'ACFAS No. 45. Association canadienne-française pour l'avancement des sciences, Québec. pp. 79-88.
  • 50
    • 0004167189 scopus 로고    scopus 로고
    • Cross-fertilization between models in phyllotaxis
    • Jean, R.V. 1998. Cross-fertilization between models in phyllotaxis. J. Biol. Syst. 7: 145-158.
    • (1998) J. Biol. Syst , vol.7 , pp. 145-158
    • Jean, R.V.1
  • 51
    • 0004274207 scopus 로고    scopus 로고
    • Jean, R.V, and Barabé, D, Editors, World Scientific, Singapore
    • Jean, R.V., and Barabé, D. (Editors). 1998a. Symmetry in plants. World Scientific, Singapore.
    • (1998) Symmetry in plants
  • 52
    • 0004167191 scopus 로고    scopus 로고
    • Phyllotaxis - the way ahead, a view on open questions and directions of research
    • doi:10.1142/S021833909800011X
    • Jean, R.V., and Barabé, D. 1998b. Phyllotaxis - the way ahead, a view on open questions and directions of research. J. Biol. Syst. 6: 95-126. doi:10.1142/S021833909800011X.
    • (1998) J. Biol. Syst , vol.6 , pp. 95-126
    • Jean, R.V.1    Barabé, D.2
  • 53
    • 0034863373 scopus 로고    scopus 로고
    • Application of two mathematical models to a family of plants with enigmatic phyllotactic processes
    • Jean, R.V., and Barabé, D. 2001. Application of two mathematical models to a family of plants with enigmatic phyllotactic processes. Ann. Bot. (Lond.), 88: 173-186.
    • (2001) Ann. Bot. (Lond.) , vol.88 , pp. 173-186
    • Jean, R.V.1    Barabé, D.2
  • 54
    • 16544392568 scopus 로고    scopus 로고
    • Statistical recognition of random and regular phyllotactic patterns
    • Jeune, B., and Barabé, D. 2004. Statistical recognition of random and regular phyllotactic patterns. Ann. Bot. (Lond.), 94: 913-917.
    • (2004) Ann. Bot. (Lond.) , vol.94 , pp. 913-917
    • Jeune, B.1    Barabé, D.2
  • 55
    • 28444448790 scopus 로고    scopus 로고
    • A stochastic approach to phyllotactic patterns analysis
    • doi:10.1016/j.jtbi.2005.05.036
    • Jeune, B., and Barabé, D. 2006a. A stochastic approach to phyllotactic patterns analysis. J. Theor. Biol. 238: 52-59. doi:10.1016/j.jtbi.2005.05.036.
    • (2006) J. Theor. Biol , vol.238 , pp. 52-59
    • Jeune, B.1    Barabé, D.2
  • 56
    • 33344472285 scopus 로고    scopus 로고
    • Simulations of transitions from regular to stochastic phyllotactic patterns
    • doi:10.1142/S0218339006001623
    • Jeune, B., and Barabé, D. 2006b. Simulations of transitions from regular to stochastic phyllotactic patterns. J. Biol. Syst. 14: 113-129. doi:10.1142/S0218339006001623.
    • (2006) J. Biol. Syst , vol.14 , pp. 113-129
    • Jeune, B.1    Barabé, D.2
  • 57
    • 2442612982 scopus 로고    scopus 로고
    • Compositions of random Möbius transformations
    • Karmakar, S., and Key, E.S. 2004. Compositions of random Möbius transformations. Stoch. Anal. Appl. 22: 525-557.
    • (2004) Stoch. Anal. Appl , vol.22 , pp. 525-557
    • Karmakar, S.1    Key, E.S.2
  • 58
    • 0042928213 scopus 로고    scopus 로고
    • Geometrical relationships specifying the phyllotactic pattern of aquatic plants
    • Kelly, W.J., and Cooke, J.T. 2003. Geometrical relationships specifying the phyllotactic pattern of aquatic plants. Am. J. Bot. 90: 1131-1143.
    • (2003) Am. J. Bot , vol.90 , pp. 1131-1143
    • Kelly, W.J.1    Cooke, J.T.2
  • 59
    • 0031823313 scopus 로고    scopus 로고
    • Explaining curd and spear geometry in broccoli, cauliflower and 'romanesco': Quantitative variation in activity of primary meristems
    • doi:10.1007/s004250050371
    • Kieffer, M., Fuller, M.P., and Jellings, A.J. 1998. Explaining curd and spear geometry in broccoli, cauliflower and 'romanesco': quantitative variation in activity of primary meristems. Planta, 206: 34-43. doi:10.1007/s004250050371.
    • (1998) Planta , vol.206 , pp. 34-43
    • Kieffer, M.1    Fuller, M.P.2    Jellings, A.J.3
  • 60
    • 2642585068 scopus 로고    scopus 로고
    • On the mystery of the golden angle in phyllotaxis
    • doi:10.1111/j.1365-3040.2004.01185.x
    • King, S., Beck, F., and Lüttge, U. 2004. On the mystery of the golden angle in phyllotaxis. Plant Cell Environ. 27: 685-695. doi:10.1111/j.1365-3040.2004.01185.x.
    • (2004) Plant Cell Environ , vol.27 , pp. 685-695
    • King, S.1    Beck, F.2    Lüttge, U.3
  • 61
    • 28444439462 scopus 로고    scopus 로고
    • Phyllotaxis as a geometrical and dynamical system
    • Edited by R.V. Jean and D. Barabé. World Scientific, Singapore, pp
    • Koch, A.-J., Bernasconi, G., and Rothen, F. 1998. Phyllotaxis as a geometrical and dynamical system. In Symmetry in plants. Edited by R.V. Jean and D. Barabé. World Scientific, Singapore, pp. 459-486.
    • (1998) Symmetry in plants , pp. 459-486
    • Koch, A.-J.1    Bernasconi, G.2    Rothen, F.3
  • 62
    • 0001902056 scopus 로고
    • Three approaches to the quantitative definition of information
    • Kolmogorov, A.N. 1965. Three approaches to the quantitative definition of information. Prob. Inform. Trans. 1: 1-7.
    • (1965) Prob. Inform. Trans , vol.1 , pp. 1-7
    • Kolmogorov, A.N.1
  • 63
    • 0035452087 scopus 로고    scopus 로고
    • Dynamical models of phyllotaxis
    • doi:10.1016/S0167-2789(01)00275-5
    • Kunz, M. 2001. Dynamical models of phyllotaxis. Physica D, 157: 147-165. doi:10.1016/S0167-2789(01)00275-5.
    • (2001) Physica D , vol.157 , pp. 147-165
    • Kunz, M.1
  • 64
    • 0039525440 scopus 로고    scopus 로고
    • Ontogenetic variation of phyllotaxis and apex geometry in vegetative shoots of Sedum maximum (L.) Hoffin
    • Kwiatkowska, D., and Florek-Marwitz, J. 1999. Ontogenetic variation of phyllotaxis and apex geometry in vegetative shoots of Sedum maximum (L.) Hoffin. Acta Soc. Bot. Poloniae, 68: 85-95.
    • (1999) Acta Soc. Bot. Poloniae , vol.68 , pp. 85-95
    • Kwiatkowska, D.1    Florek-Marwitz, J.2
  • 65
    • 34248361333 scopus 로고
    • Characterization of three apical meristems mutants of Arabidopsis thaliana
    • Leyser, H.M.O., and Furner, I.J. 1992. Characterization of three apical meristems mutants of Arabidopsis thaliana. Development, 122: 87-96.
    • (1992) Development , vol.122 , pp. 87-96
    • Leyser, H.M.O.1    Furner, I.J.2
  • 66
    • 11744320382 scopus 로고    scopus 로고
    • Phyllotaxis: Its geometry and dynamics
    • Liaw, S.S. 1998. Phyllotaxis: its geometry and dynamics. Physiol. Rev. 57: 4589-4593.
    • (1998) Physiol. Rev , vol.57 , pp. 4589-4593
    • Liaw, S.S.1
  • 67
    • 0010409817 scopus 로고    scopus 로고
    • The living spiral - a dimensionless biological constant gives a new perspective to physics
    • Lieber, M.M. 1998. The living spiral - a dimensionless biological constant gives a new perspective to physics. Riv. Biol. Biol. Forum, 91: 91-118.
    • (1998) Riv. Biol. Biol. Forum , vol.91 , pp. 91-118
    • Lieber, M.M.1
  • 69
    • 0000453956 scopus 로고
    • Energy spectra of quasiperiodic sytems via information entropy
    • Macia, E., Domínguez-Adame, F., and Sánchez, A. 1994. Energy spectra of quasiperiodic sytems via information entropy. Physiol. Rev. 50: 679-682.
    • (1994) Physiol. Rev , vol.50 , pp. 679-682
    • Macia, E.1    Domínguez-Adame, F.2    Sánchez, A.3
  • 70
    • 0347656782 scopus 로고    scopus 로고
    • Structural theory of phyllotaxis. I. The mechanism of formation of the spiral structures of alternate phyllotaxis
    • Malygin, A.G. 1998. Structural theory of phyllotaxis. I. The mechanism of formation of the spiral structures of alternate phyllotaxis. Biofizika, 43: 335-342.
    • (1998) Biofizika , vol.43 , pp. 335-342
    • Malygin, A.G.1
  • 71
    • 0041118453 scopus 로고    scopus 로고
    • Structural theory in phyllotaxis. II. Interrelation between lower and superior phyllotaxis forms
    • Malygin, A.G. 2000. Structural theory in phyllotaxis. II. Interrelation between lower and superior phyllotaxis forms. Biofizika, 45: 1112-1118.
    • (2000) Biofizika , vol.45 , pp. 1112-1118
    • Malygin, A.G.1
  • 72
    • 38249037824 scopus 로고
    • Phyllotaxis as a dissipative structure
    • Marzec, C. 1987. Phyllotaxis as a dissipative structure. Math. Model. 8: 740-745.
    • (1987) Math. Model , vol.8 , pp. 740-745
    • Marzec, C.1
  • 73
    • 0347415175 scopus 로고    scopus 로고
    • Uniform spacing models for the morphogenesis of high symmetry biological structures: Icosahedral capsids, coaxial helices, and helical phyllotaxis
    • Edited by R.V. Jean and D. Barabé. World Scientific, Singapore. pp
    • Marzec, C. 1998. Uniform spacing models for the morphogenesis of high symmetry biological structures: icosahedral capsids, coaxial helices, and helical phyllotaxis. In Symmetry in plants. Edited by R.V. Jean and D. Barabé. World Scientific, Singapore. pp. 681-722.
    • (1998) Symmetry in plants , pp. 681-722
    • Marzec, C.1
  • 74
    • 0004060629 scopus 로고    scopus 로고
    • A pragmatic approach to modelling morphogenesis
    • doi:10.1142/S0218339099000218
    • Marzec, C. 1999a. A pragmatic approach to modelling morphogenesis. J. Biol. Syst. 7: 333-351. doi:10.1142/S0218339099000218.
    • (1999) J. Biol. Syst , vol.7 , pp. 333-351
    • Marzec, C.1
  • 75
    • 0346789698 scopus 로고    scopus 로고
    • The morphogenesis of high symmetry: The warping theorem
    • doi:10.1142/S021833909900022X
    • Marzec, C. 1999b. The morphogenesis of high symmetry: the warping theorem. J. Biol. Syst. 7: 353-427. doi:10.1142/S021833909900022X.
    • (1999) J. Biol. Syst , vol.7 , pp. 353-427
    • Marzec, C.1
  • 76
    • 0038071794 scopus 로고    scopus 로고
    • Complex pattern formation by a self-destabilization of established patterns: Chemotactic orientation and phyllotaxis as examples
    • Meinhardt, H. 2003. Complex pattern formation by a self-destabilization of established patterns: chemotactic orientation and phyllotaxis as examples. C.R. Biol.326: 223-237.
    • (2003) C.R. Biol , vol.326 , pp. 223-237
    • Meinhardt, H.1
  • 77
    • 9644257135 scopus 로고    scopus 로고
    • Out-of-phase oscillations and traveling waves with unusual properties: The use of three-component systems in biology
    • doi:10.1016/j.physd.2004.08.018
    • Meinhardt, H. 2004. Out-of-phase oscillations and traveling waves with unusual properties: the use of three-component systems in biology. Physica D, 199: 264-277. doi:10.1016/j.physd.2004.08.018.
    • (2004) Physica D , vol.199 , pp. 264-277
    • Meinhardt, H.1
  • 78
    • 0041381389 scopus 로고    scopus 로고
    • Continuum elasticity with topological defects, including dislocations and extra-matter
    • Miri, M., and Rivier, N. 2002. Continuum elasticity with topological defects, including dislocations and extra-matter. J. Phys. A Math. Gen. 35: 1727-1739.
    • (2002) J. Phys. A Math. Gen , vol.35 , pp. 1727-1739
    • Miri, M.1    Rivier, N.2
  • 79
    • 4444312646 scopus 로고    scopus 로고
    • Molecular and genetic interactions between STYLOSA and GRAMINIFOLIA in the control of Antirrhinum vegetative and reproductive development
    • doi:10.1242/dev.01205
    • Navarro, C., Efremova, N., Golz, J.F., Rubiera, R., Kuckenberg, M., Castillo, R., Tietz, O., Saedler, H., and Schwarz-Sommer, Z. 2004. Molecular and genetic interactions between STYLOSA and GRAMINIFOLIA in the control of Antirrhinum vegetative and reproductive development. Development, 131: 3649-3659. doi:10.1242/dev.01205.
    • (2004) Development , vol.131 , pp. 3649-3659
    • Navarro, C.1    Efremova, N.2    Golz, J.F.3    Rubiera, R.4    Kuckenberg, M.5    Castillo, R.6    Tietz, O.7    Saedler, H.8    Schwarz-Sommer, Z.9
  • 80
    • 0008212477 scopus 로고    scopus 로고
    • Light harvesting "fitness landscape" for vertical shoots with different phyllotactic systems
    • Edited by R.V. Jean and D. Barabé. World Scientific, Singapore. pp
    • Niklas, K.J. 1998. Light harvesting "fitness landscape" for vertical shoots with different phyllotactic systems. In Symmetry in plants. Edited by R.V. Jean and D. Barabé. World Scientific, Singapore. pp. 759-773.
    • (1998) Symmetry in plants , pp. 759-773
    • Niklas, K.J.1
  • 81
    • 0035999894 scopus 로고    scopus 로고
    • OsPNH1 regulates leaf development and maintenance of the shoot apical meristem in rice
    • doi:10.1046/j.1365-313X.2002. 01279.x
    • Nishimura, A., Ito, M., Kamiya, N., Sato, Y., and Matsuoka, M. 2002. OsPNH1 regulates leaf development and maintenance of the shoot apical meristem in rice. Plant J. 30: 189-201. doi:10.1046/j.1365-313X.2002. 01279.x.
    • (2002) Plant J , vol.30 , pp. 189-201
    • Nishimura, A.1    Ito, M.2    Kamiya, N.3    Sato, Y.4    Matsuoka, M.5
  • 82
    • 33751239966 scopus 로고    scopus 로고
    • Topological entropy and the preimage structure of maps
    • Nitecki, Z.H. 2003-2004. Topological entropy and the preimage structure of maps. Real Anal. Exchange, 29: 9-42.
    • (2003) Real Anal. Exchange , vol.29 , pp. 9-42
    • Nitecki, Z.H.1
  • 83
    • 0035143177 scopus 로고    scopus 로고
    • REVOLUTA regulates meristem initiation at lateral positions
    • doi:10.1046/j.1365-313x.2001.00959.x
    • Otsuga, D., DeGuzman, B., Prigge, M.J., Drews, G.N., and Clark, S.E. 2001. REVOLUTA regulates meristem initiation at lateral positions. Plant J. 25: 223-236. doi:10.1046/j.1365-313x.2001.00959.x.
    • (2001) Plant J , vol.25 , pp. 223-236
    • Otsuga, D.1    DeGuzman, B.2    Prigge, M.J.3    Drews, G.N.4    Clark, S.E.5
  • 84
    • 2642517646 scopus 로고    scopus 로고
    • Dynamical system approach to phyllotaxis
    • Ovidio, F., and Mosekilde, E. 2000. Dynamical system approach to phyllotaxis. Phys. Rev. E, 61: 354-365.
    • (2000) Phys. Rev. E , vol.61 , pp. 354-365
    • Ovidio, F.1    Mosekilde, E.2
  • 86
    • 0035540278 scopus 로고    scopus 로고
    • Genesis of morphometric invariants of higher plants as a database for the genesis of morphometric invariants of vertebrates
    • doi:10.1023/A:1012577012722
    • Petrov, E.A. 2001. Genesis of morphometric invariants of higher plants as a database for the genesis of morphometric invariants of vertebrates. Russ. J. Plant Physiol. 48: 825-827. doi:10.1023/A:1012577012722.
    • (2001) Russ. J. Plant Physiol , vol.48 , pp. 825-827
    • Petrov, E.A.1
  • 87
    • 0036353826 scopus 로고    scopus 로고
    • Two notions of conspicuity and the classification of phyllotaxis
    • doi:10.1006/jtbi.2002.2527
    • Reick, C.H. 2002. Two notions of conspicuity and the classification of phyllotaxis. J. Theor. Biol. 215: 263-271. doi:10.1006/jtbi.2002.2527.
    • (2002) J. Theor. Biol , vol.215 , pp. 263-271
    • Reick, C.H.1
  • 88
    • 0010865294 scopus 로고    scopus 로고
    • Phyllotaxis in higher plants
    • Edited by M.T. McManus and B.E. Veit. CRC Press, Boca Raton, Fla. pp
    • Reinhardt, D., and Kuhlemeier, C. 2001. Phyllotaxis in higher plants. In Meristematic tissues in plant growth and development. Edited by M.T. McManus and B.E. Veit. CRC Press, Boca Raton, Fla. pp. 172-212.
    • (2001) Meristematic tissues in plant growth and development , pp. 172-212
    • Reinhardt, D.1    Kuhlemeier, C.2
  • 89
    • 0032170390 scopus 로고    scopus 로고
    • Localized upregulation of a new expansion gene predicts the site of leaf formation in the tomato meristem
    • doi:10.1105/tpc.10.9.1427
    • Reinhardt, D., Witter, F., Mandel, T., and Kuhlemeier, C. 1998. Localized upregulation of a new expansion gene predicts the site of leaf formation in the tomato meristem. Plant Cell, 10: 1427-1437. doi:10.1105/tpc.10.9.1427.
    • (1998) Plant Cell , vol.10 , pp. 1427-1437
    • Reinhardt, D.1    Witter, F.2    Mandel, T.3    Kuhlemeier, C.4
  • 90
    • 0034020523 scopus 로고    scopus 로고
    • Auxin regulates the initiation and radial position of plant lateral organs
    • doi:10.1105/tpc.12.4.507
    • Reinhardt, D., Mandel, T., and Kuhlemeier, C. 2000. Auxin regulates the initiation and radial position of plant lateral organs. Plant Cell, 12: 507-518. doi:10.1105/tpc.12.4.507.
    • (2000) Plant Cell , vol.12 , pp. 507-518
    • Reinhardt, D.1    Mandel, T.2    Kuhlemeier, C.3
  • 92
    • 13444256462 scopus 로고    scopus 로고
    • Microsurgical and laser ablation analysis of leaf positioning and dorsoventral patterning in tomato
    • Reinhardt, D., Frenz, M., Mandel, T., and Kuhlemeier, C. 2005. Microsurgical and laser ablation analysis of leaf positioning and dorsoventral patterning in tomato. Development, 132: 15-26.
    • (2005) Development , vol.132 , pp. 15-26
    • Reinhardt, D.1    Frenz, M.2    Mandel, T.3    Kuhlemeier, C.4
  • 93
    • 0037734298 scopus 로고    scopus 로고
    • What do we mean by biological complexity?
    • Ricard, J. 2003. What do we mean by biological complexity? C.R. Biol. 326: 133-140.
    • (2003) C.R. Biol , vol.326 , pp. 133-140
    • Ricard, J.1
  • 94
    • 0001286925 scopus 로고
    • Phyllotaxis: Its quantitative expression and relation to growth in the apex
    • Richards, F.J. 1951. Phyllotaxis: its quantitative expression and relation to growth in the apex. Philos. Trans. R. Soc. Lond. B Biol. Sci. 235: 509-564.
    • (1951) Philos. Trans. R. Soc. Lond. B Biol. Sci , vol.235 , pp. 509-564
    • Richards, F.J.1
  • 95
    • 0000146492 scopus 로고    scopus 로고
    • Plastochrone ratio and leaf arc as parameters of a quantitative phyllotaxis analysis in vascular plants
    • Edited by R.V. Jean and D. Barabé. World Scientific, Singapore. pp
    • Rutishauzer, R. 1998. Plastochrone ratio and leaf arc as parameters of a quantitative phyllotaxis analysis in vascular plants. In Symmetry in plants. Edited by R.V. Jean and D. Barabé. World Scientific, Singapore. pp. 171-212.
    • (1998) Symmetry in plants , pp. 171-212
    • Rutishauzer, R.1
  • 96
    • 0029417232 scopus 로고
    • The diversity in shoot morphology of herbaceous plants in relation to solar radiation captured by leaves
    • doi:10.1006/jtbi.1995.0246
    • Sekimura, T. 1995. The diversity in shoot morphology of herbaceous plants in relation to solar radiation captured by leaves. J. Theor. Biol. 177: 289-297. doi:10.1006/jtbi.1995.0246.
    • (1995) J. Theor. Biol , vol.177 , pp. 289-297
    • Sekimura, T.1
  • 97
    • 3042525010 scopus 로고    scopus 로고
    • Quasicrystalline pattern formation in fluid substrates and phyllotaxis
    • Edited by R.V Jean and D. Barabé. World Scientific, Singapore. pp
    • Selvam, A.M. 1998. Quasicrystalline pattern formation in fluid substrates and phyllotaxis. In Symmetry in plants. Edited by R.V Jean and D. Barabé. World Scientific, Singapore. pp. 795-809.
    • (1998) Symmetry in plants , pp. 795-809
    • Selvam, A.M.1
  • 99
    • 2942581565 scopus 로고    scopus 로고
    • Phyllotactic patterns of plants
    • Shipman, P.D., and Newell, A.C. 2004. Phyllotactic patterns of plants. Phys. Rev. Lett. 92(16): 168102-1-168102-4.
    • (2004) Phys. Rev. Lett , vol.92 , Issue.16
    • Shipman, P.D.1    Newell, A.C.2
  • 101
    • 0036741494 scopus 로고    scopus 로고
    • Disruption of a DNA topoisomerase I gene affects morphogenesis in Arabidopsis
    • doi:10.1105/tpc.001925
    • Takahashi, T., Matsuhara, S., Abe, M., and Komeda, Y. 2002. Disruption of a DNA topoisomerase I gene affects morphogenesis in Arabidopsis. Plant Cell, 14: 2085-2093. doi:10.1105/tpc.001925.
    • (2002) Plant Cell , vol.14 , pp. 2085-2093
    • Takahashi, T.1    Matsuhara, S.2    Abe, M.3    Komeda, Y.4
  • 102
    • 0033166090 scopus 로고    scopus 로고
    • Transgenic tobacco over-expressing a homeobox gene shows a developmental interaction between leaf morphogenesis and phyllotaxy
    • Tamaoki, M., Nishimura, A., Aida, M., Tasaka, M., and Matsuoka, M. 1999. Transgenic tobacco over-expressing a homeobox gene shows a developmental interaction between leaf morphogenesis and phyllotaxy. Plant Cell Physiol. 40: 657-667.
    • (1999) Plant Cell Physiol , vol.40 , pp. 657-667
    • Tamaoki, M.1    Nishimura, A.2    Aida, M.3    Tasaka, M.4    Matsuoka, M.5
  • 103
    • 38249014202 scopus 로고
    • A gene profoundly affecting shoot organization in the early phase of rice develpment
    • doi:10.1016/0168-9452(92)90011-A
    • Tamura, Y., Kitano, H., Satoh, H., and Nagato, Y. 1992. A gene profoundly affecting shoot organization in the early phase of rice develpment. Plant Sci. 82: 91-99. doi:10.1016/0168-9452(92)90011-A.
    • (1992) Plant Sci , vol.82 , pp. 91-99
    • Tamura, Y.1    Kitano, H.2    Satoh, H.3    Nagato, Y.4
  • 104
    • 0037193709 scopus 로고    scopus 로고
    • Traas, J., and Vernoux, T. 2002. The shoot apical meristem: the dynamics of a stable structure. Philos. Trans. R. Soc. B Biol. Sci 357: 737-747.
    • Traas, J., and Vernoux, T. 2002. The shoot apical meristem: the dynamics of a stable structure. Philos. Trans. R. Soc. B Biol. Sci 357: 737-747.
  • 105
    • 0009125939 scopus 로고    scopus 로고
    • Changes in phyllotactic pattern structure in Pinus due to changes in altitude
    • Edited by R.V. Jean and D. Barabé. World Scientific, Singapore. pp
    • Vakarelov, I. 1998. Changes in phyllotactic pattern structure in Pinus due to changes in altitude. In Symmetry in plants. Edited by R.V. Jean and D. Barabé. World Scientific, Singapore. pp. 213-230.
    • (1998) Symmetry in plants , pp. 213-230
    • Vakarelov, I.1
  • 106
    • 7244223420 scopus 로고    scopus 로고
    • Leaf phyllotaxis: Does it really affect light capture?
    • Valladares, F., and Brites, D. 2004. Leaf phyllotaxis: does it really affect light capture? Plant Ecol. 174: 11-17.
    • (2004) Plant Ecol , vol.174 , pp. 11-17
    • Valladares, F.1    Brites, D.2
  • 107
    • 0036677771 scopus 로고    scopus 로고
    • Convergence in light capture efficiencies among tropical forest understory plants with contrasting crown architectures: A case of morphological compensation
    • Valladares, F., Skillman, J.B., and Pearcy, R.W. 2002. Convergence in light capture efficiencies among tropical forest understory plants with contrasting crown architectures: a case of morphological compensation. Am. J. Bot. 89: 1275-1284.
    • (2002) Am. J. Bot , vol.89 , pp. 1275-1284
    • Valladares, F.1    Skillman, J.B.2    Pearcy, R.W.3
  • 109
    • 0007404696 scopus 로고
    • Diffusion mechanism for phyllotaxis, theoretical, physico-chemical and computer study
    • Veen, A.H., and Lindenmayer, A. 1977. Diffusion mechanism for phyllotaxis, theoretical, physico-chemical and computer study. Plant Physiol. 60: 127-139.
    • (1977) Plant Physiol , vol.60 , pp. 127-139
    • Veen, A.H.1    Lindenmayer, A.2
  • 110
    • 0032516152 scopus 로고    scopus 로고
    • Regulation of leaf initiation by terminal earl gene of maize
    • doi:10.1038/30239
    • Veit, B., Briggs, S.P., Schmidt, R.J., Yanofsky, M.F., and Hake, S. 1998. Regulation of leaf initiation by terminal earl gene of maize. Nature, 393: 166-168. doi:10.1038/30239.
    • (1998) Nature , vol.393 , pp. 166-168
    • Veit, B.1    Briggs, S.P.2    Schmidt, R.J.3    Yanofsky, M.F.4    Hake, S.5
  • 111
    • 0026776230 scopus 로고
    • LEAFY controls floral meristem identity in Arabidopsis
    • doi:10.1016/0092-8674(92)90295-N
    • Weigel, D., Alvarez, J., Smyth, D.R., Yanofsky, M.F., and Meyerowitz, E.M. 1992. LEAFY controls floral meristem identity in Arabidopsis. Cell, 69: 843-859. doi:10.1016/0092-8674(92)90295-N.
    • (1992) Cell , vol.69 , pp. 843-859
    • Weigel, D.1    Alvarez, J.2    Smyth, D.R.3    Yanofsky, M.F.4    Meyerowitz, E.M.5
  • 112
  • 114
    • 0029621252 scopus 로고
    • The geometry of golden section phyllotaxis
    • Wilson, P.I. 1995. The geometry of golden section phyllotaxis. J. Theor. Biol. 177: 315-323.
    • (1995) J. Theor. Biol , vol.177 , pp. 315-323
    • Wilson, P.I.1
  • 115
    • 0012293957 scopus 로고
    • On the structural complexity of simple biosystems
    • Yagil, G. 1985. On the structural complexity of simple biosystems. J. Theor. Biol. 112: 1-23.
    • (1985) J. Theor. Biol , vol.112 , pp. 1-23
    • Yagil, G.1
  • 116
    • 3042695168 scopus 로고    scopus 로고
    • Sequences of symmetry-breaking in phyllotactic transitions
    • doi:10.1016/j.bulm.2003.10.006
    • Yamada, H., Tanaka, R., and Nakagaki, T. 2004. Sequences of symmetry-breaking in phyllotactic transitions. Bull. Math. Biol. 66: 779-789. doi:10.1016/j.bulm.2003.10.006.
    • (2004) Bull. Math. Biol , vol.66 , pp. 779-789
    • Yamada, H.1    Tanaka, R.2    Nakagaki, T.3
  • 117
    • 0347931774 scopus 로고    scopus 로고
    • A growth-controlled model of the shape of a sunflower head
    • doi:10.1016/j.mbs.2003.09.002
    • Yeatts, F.R. 2004. A growth-controlled model of the shape of a sunflower head. Math. Biosci. 187: 205-221. doi:10.1016/j.mbs.2003.09.002.
    • (2004) Math. Biosci , vol.187 , pp. 205-221
    • Yeatts, F.R.1
  • 118
    • 0036802329 scopus 로고    scopus 로고
    • A simulation study on the importance of size-related changes in leaf morphology and physiology for carbon gain in an epiphytic bromeliad
    • Zotz, G., Reichling, P., and Valladares, F. 2002. A simulation study on the importance of size-related changes in leaf morphology and physiology for carbon gain in an epiphytic bromeliad. Ann. Bot. (Lond.), 90: 437-443.
    • (2002) Ann. Bot. (Lond.) , vol.90 , pp. 437-443
    • Zotz, G.1    Reichling, P.2    Valladares, F.3


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