archetypes used for the drawing of celebrated wall paintings

We have studied, first, the great wall painting consisting of geometric themes, initially decorating the internal murals of the uppermost floor of Xeste 3. the stability of contour lines of most depicted spirals imposed the idea that guides had been probably used for the their drawing. Examples of drawn spiral images:

We have tested various candidate geometric archetypes, such the exponential/logarithmic spiral, the involute of a circle, namely the spiral generated by unwrapping a thread around a peg, the Archimedes/linear spiral etc. all archetypes have been rejected as potential archetypes, except the Archimedes spiral that fits the spirals contour exceptionally well in a piece-wise manner. [Papaodysseus C., Panagopoulos Ath., Exarhos M., Triantafullou C., Roussopoulos G., Roussopoulos P., Fragoulis D., Galanopoulos G., Vlahopoulos A., Doumas C., “Distinct, Late Bronze Age (c. 1650 BC) Wall-paintings of Akrotiri, Thera, Comprising Advanced Geometrical Patterns,” Archaeometry. (In press, October 2005)],[C. Papaodysseus, M. Exarhos, Th. Panagopoulos, C. Triantafillou, G. Roussopoulos, Af. Pantazi, V. Loumos, D. Fragoulis, C. Doumas, Identification of Geometrical Shapes in Paintings and its Application to Demonstrate the Foundations of Geometry in 1650 BC, IEEE Transactions on Image Processing, Vol. 14, No. 7, July 2005]. We note that the conception of linear spiral was so far attributed to Conon from Samos (Κόνων) and his friend Archimedes at circa 300 B.C. namely 1.400 years after the Late Bronze Age Akrotiri civilization.

The exact method they employed for constructing the linear spiral archetype is unknown. However, one cannot exclude that they employed the following geometric method for generating points of a linear spiral [Papaodysseus C., Panagopoulos Ath., Exarhos M., Triantafullou C., Roussopoulos G., Roussopoulos P., Fragoulis D., Galanopoulos G., Vlahopoulos A., Doumas C., “Distinct, Late Bronze Age (c. 1650 BC) Wall-paintings of Akrotiri, Thera, Comprising Advanced Geometrical Patterns,” Archaeometry. (In press, October 2005)],[C. Papaodysseus, M. Exarhos, Th. Panagopoulos, C. Triantafillou, G. Roussopoulos, Af. Pantazi, V. Loumos, D. Fragoulis, C. Doumas, Identification of Geometrical Shapes in Paintings and its Application to Demonstrate the Foundations of Geometry in 1650 BC, IEEE Transactions on Image Processing, Vol. 14, No. 7, July 2005]:

The circles are equidistant and the straight lines divide the entire 360o angle in N equal angles.

We further pursued the previous hypothesis, although the division of the entire 360o angle in N equal angles requires an advanced sense of geometry and related experimentation. Hence, we have looked for decorative elements in the wall painting that belong to equiangular lines. Thus by application of novel developed algorithms, we have found numerous ensembles of decorative elements belonging to radii of regular 48-polygons, 32-polygons, 24-polygons etc. [Papaodysseus C., Panagopoulos Ath., Exarhos M., Triantafullou C., Roussopoulos G., Roussopoulos P., Fragoulis D., Galanopoulos G., Vlahopoulos A., Doumas C., “Distinct, Late Bronze Age (c. 1650 BC) Wall-paintings of Akrotiri, Thera, Comprising Advanced Geometrical Patterns,” Archaeometry. (In press, October 2005)],[C. Papaodysseus, M. Exarhos, Th. Panagopoulos, C. Triantafillou, G. Roussopoulos, Af. Pantazi, V. Loumos, D. Fragoulis, C. Doumas, Identification of Geometrical Shapes in Paintings and its Application to Demonstrate the Foundations of Geometry in 1650 BC, IEEE Transactions on Image Processing, Vol. 14, No. 7, July 2005]p>

Decorative elements laying on radii of regular polygon of 48 sides

Decorative elements laying on radii of regular polygon of 32 sides

The stability of the contour line in major figures of other wall paintings with no geometric thematic content, generated the idea that these contour lines may have been also drawn by means guides, which correspond to geometric archetypes.
We have developed and applied novel algorithms, which show that all contour lines of many wall paintings have been generated by means of the following guides [Papaodysseus C., Fragoulis D., Panagopoulos M., Panagopoulos T., Rousopoulos P., Exarhos M., Skembris A., «Determination of the Method of Construction of 1650 B.C. Wall Paintings», IEEE Trans. on PAMI, pp. 1361-1371, vol. 28, Sept. 2006 ],[Fragoulis D., Skembris A., Papaodysseus C., Rousopoulos P., Panagopoulos Th., Triantafyllou C., Vlachopoulos A. , Doumas C., "Origins and Application of Geometry in the Thera Prehistoric Civilization Ca. 1650 BC" Centaurus, pp. 316-340, Vol. 47, No. 4. (October 2005)]

An Archimedes/linear spiral always depicted in red.

Four hyperbolae (in cm): a=14.24, b=20.12 (magenta), a=4.11, b=6.29 (green), a=7.86, b=17.63 (blue), a=2.09, b=2.52 (cyan).

All major figures of the celebrated wall painting gotheriing of Crocus were made via the use of the above guides/stencils:

p.154 Doumas, C., 1991.The Wall Paintings of Thera. Athens, The Thera Foundation

The colors of the computer-generated lines strictly correspond to the proper previously defined guides. For example, all contour lines shown in red correspond to the specific Archimedes spiral

p.156 Doumas, C., 1991.The Wall Paintings of Thera. Athens, The Thera Foundation

All major figures of the celebrated wall painting Naked Boys also were made by using the same guides/stencils:

p.151 Doumas, C., 1991.The Wall Paintings of Thera. Athens, The Thera Foundation

p.148 Doumas, C., 1991.The Wall Paintings of Thera. Athens, The Thera Foundation

The well known wall painting wild duck may also be drawn by means of the same stencils

p.172 Doumas, C., 1991.The Wall Paintings of Thera. Athens, The Thera Foundation