Spiral formed Capricornes

Who wants to watch Astrophytum capricorne (Dietrich) Britton & Rose in its Mexican native country as a starting point Saltillo, the capital of Coahuila, votes best. From here are short ways to many interesting locations where one can admire the variability of these beautiful plants. Their habitats already start at the outskirts only just behind the industrial buildings of Ramos Arizpe. Rinconada, location of the first Capricorne find by POSELGER 1851, is only half a hour's drive away and Astrophytum capricorne v. minus (Runge & Quehl) Okumura at General Cepeda can easily be reached in an afternoon. The mountains at Arteaga also invite to a rewarding excursion. At the national highway no. 57 from Saltillo to Monclova finally, one practically find plants on the left and on the right of the road in many places. The spiral formed Astrophytums which are introduced in this contribution also are at home in this area.

Helically revolved Capricornes are seldom and usually the result of longer periods of drought. This cause presumably doesn't apply to the plants shown. They grow in an untouched area healthy and without water shortage in the midst of her normal formed relatives. Astrophytum capricorne usually settles a rocky area at easily inclined slopes. Here it grows surprising in a flat, sandy arroyo, crossed by the highway. It has essentially the characteristics of the type plants of Rinconada but tends however to a strong spine reduction. Except shooting specimens all Capricornes up to a height of 40 centimeters have eight straight ribs. Also isolated dead, dried out individuals on the area aren't coiled. So the assumption seems reasonable that the spiral forms introduced in the figure are term of individual disposition. A divergence angle differing from the ideal leaf arrangement might be the reason for it (BUXBAUM, see diagrams). BILHUBER mentions as a possibility for such a growing an inner physiological tension. However, beside theoretical considerations these are splendid plants, leaving an unforgettable impression by their visual phenomenon on everybody standing before them.

Figure texts:

Form 1
At water shortage Astrophytums often become sharp-ribbed and start to reduce their body volume by coiled growth. One then describes them as so-called hunger forms. This cause presumably isn't correct at the Astrophytum capricorne shown. It is in a good diet state for the location conditions.

Form 2
Astrophytum capricorne is usually concealed by spines so thick that it has to be distinguished hardly by the grass of the surroundings. The plants are protected from her natural eating enemies by visual mimicry excellently. It behaves different at the population with spine reduction introduced in this contribution. It was therefore possible to take a photograph of the distinctive left spiraled rib edges from a top view.

Form 3
This about 40 centimeters high Astrophytum capricorne was also coiled in his youth, but developed in the last decades again a normal growth. The hole in the lower body half (arrow) is lived in by a spider ("black widow" Latrodectus mactans). Unfortunately, she escaped the photo appointment and waited for the trouble by the European intruder in her unusual hiding-place.

Literature statement:
for the leaf arrangement and rib formation

BILHUBER, E. (1933): Beiträge zur Kenntnis der Organstellungen im Pflanzenreich, Akademische Verlagsgesellschaft m.b.H.Botanisches Archiv 35 (3): 188-250

BUXBAUM, F. (1950): Morphology of Cacti, Abbey Garden Press, Pasadena: 29-33

BUXBAUM, F. in KRAINZ, H. (1957): Die Kakteen, Franckh'sche Verlagshandlung, Stuttgart: Morphologie (8), 15.01.1957

CHEASON, D. (1990): Maths and Mamms, Brit. Cact. Succ. Journ. (GB) 8 (3): 81

HOOCK, H. (1990): Astrophytum ornatum (DE CANDOLLE) WEBER am Rio Torre Blanca, Kakt. and. Sukk. 41 (10): 230-232

MINDT, H. (1967): Die Mathematik der Spiralzeilen und das Gesetz optimaler Ästhetik, Kakt. and. Sukk. 18 (10): 184

MINDT, H. (1967): Die Mathematik der Spiralzeilen und das Gesetz optimaler Ästhetik, Kakt. and. Sukk. 18 (9): 162

RAUH, W. (1979): Kakteen an ihren Standorten, Verlag Paul Parey, Berlin und Hamburg: 23-26

SANCHEZ-MEJORADA, H. (1964): Las Matematicas de las Cactaceas, Cact. Suc. Mex. 9 (2): 38-48

SCHUMANN, K. (1897): Über die Anreihung der Warzen in der Gattung Mamillaria, Monatsschrift d. DKG, 7 (8): 113-117

STRASBURGER, E. (1983): Lehrbuch der Botanik, Gustav Fischer Verlag, Stuttgart/New York; 32. Auflage: 138-144

Texts for the dispersed leaf arrangement and rib formation

Diagram 1:
Only one areole is advertised at the dispersed leaf arrangement at every knot, in which the older one is moved respectively around a certain angle to the next young. In diagram 1 it is marked the imaginary connecting line from knot to knot as a spiral.

Diagram 2:
At the ideal 3/8 leaf arrangement of Astrophytum capricorne (Dietrich) Br.& R. eight straight ribs are the result. The connecting line of areole to areole isn't drawn for reasons of a clear overview in this diagram.

Diagram 3:
If the fraction only differs insignificantly from the mathematical ideal value 3/8, revolved ribs develop helically. The direction of rotation depends, whether the fraction is a little larger (represented here: 3/8.01 forms a right-hand helix) or smaller (for e.g. 3/7.99 forms a left-hand helix).

Diagram 4:
Increasing the fraction 2/5 to 3/8, 5/13, 8/21, 13/34... (Fibonacci series) one reaches the so-called limit divergence angle. It can roughly be characterized by the fraction 34/89 represented in the diagram. Higher fractions than 5/13 occur at Astrophyten only in transitional stages to crested plants. 2/5 and 3/8 leaf arrangements are typical of this genus.

Figures:
Astrophytum capricorne, spiralförmig / spiral formed (1)
Astrophytum capricorne, spiralförmig / spiral formed (2)
Astrophytum capricorne, spiralförmig / spiral formed (3)
Astrophytum capricorne, spiralförmig / spiral formed (4)
Diagramm / diagram 1
Diagramm / diagram 2
Diagramm / diagram 3
Diagramm / diagram 4

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