103 AN ATTEMPT AT COMPUTER ANALYSIS DETERMINATION OF CALIFORNIA ROCK ART STYLES Mary Pori and Robert F. Heizer In 1972-73 while one of us (RFH) was a Fellow at the Center for Advanced Study in the Behavioral Sciences, and the other (MP) was on the Computer staff of the Center, we decided to try to test some of the admittedly intuitive conclusions on petroglyph and pictograph style areas in California which had been proposed in a study then in press and now published (Heizer and Clewlow 1973). We thought the test to be a worthwhile undertaking since it might yield an independent check of the validity of the obviously broad categories of design elements into which the abundance of data from California rock art sites had been compressed. Our reasons for classifying all California pecked and painted rock art design elements into five classes or groups (Human, Animal, Circle and Dot, Angular, Curvilinear) have been stated elsewhere (Heizer and Clewlow 1973:9-10), and while we were not very comfortable in having taken this route, we nevertheless saw it as the only practicable one available to treat the very complicated mass of design element data. Some classification of rock art design elements is mandatory, the choices of how to accomplish this are wide, and for better or worse we decided on a scheme which seemed to us to be practicable. Our conclusions, based in part on element frequencies, and in part upon our intuitive assessment based on familiarity with the design elements of how the totality of forms of pecked or painted designs corresponded with geography, were represented in two maps on which petroglyph and pictograph style areas were shown (Heizer and Clewlow 1973:Maps 15, 16). These maps are reproduced here in Figs. 8 and 9. Examples of statistical methods applied to petroglyph data for the purpose of differentiating styles within one site, or among a series of sites, are rare-- among those known to us are the attempts by Lorandi di Gieco (1965), von Werlhof (1965:91-115), Maggs (1967), Heizer and Baumhoff (1962:198-199). None of these are like the analysis presented here. One method of discriminating style areas of rock art is provided by the method known as multidimensional scaling. In order to illustrate the ways in which this technique can be applied to an archaeological problem, the results of scaling 37 California counties based on petroglyph elements and 23 Califor- nia counties based on pictograph elements are presented. We have information on the occurrence of pictographs in 23 California counties. Let us assign a unique identification, number between I and 23 to each county. We base this assignment on an alphabetic ordering of the counties. 104 Thus, 1 = Amador 2 = Calaveras 3 = Fresno 23 = Tuolumne The first step in scaling N objects is the computation of an N by N proximity matrix X. In this case our objects are California counties; for pictographs, N=23. A proximity matrix is simply a two dimensional array of numbers; the (i-j)th element of X, xi*, is a measure of association between the ith and jth objects (counties). In analyzing pictographs, we must first compute a 23 by 23 proximity matrix: 1 1 2 1 3 1 23 2 1 2 2 2 3 X2 23 X = \ . ~ ~~~~~~ . 0 X 23 1 23 2 23 3 23 23 where x** is a measure of how similar the ith and jth counties are. For example, x indicates the degree of similarity between Amador and Calaveras counties, wgile x indicates the degree of similarity between Amador and Tuolumne counties. i little thought reveals that the proximity matrix is symmetric, as xi = xj, e.g., the degree of similarity between Amador and Calaveras counties is identical to the degree of similarity between Calaveras and Amador coutnies. As is often characteristic of mathematical reasoning, what seems obtuse in the abstract, sounds like tautology when discussed in terms of a lyecific case. Many different measures of association have been suggested, and there are many unresolved problems in choosing such a metric. However, since it is not the purpose of this paper to enter into a discussion of the advantages and disadvantages of the various measures which could be used, we shall move on to a definition of the metrics actually used. Two different types of metrics were employed: (1) a modified version of the chi-square goodness-of-fit statistic; and (2) an indicator function indicating the niumber of similar categories. I/ -A summary of these can be found in Kendall and Stuart., 1959.. 105 Specifically, assume that we have K different categories into which we can classify a given element. In the case of California rock art, K=5: human, animal, circle and dot, angular, and curvilinear. Let n be the number of elements in the jth category found in the ith object to U scaled. For example, n3 is the number of elements in the second category (animal) found in the t1aird county (Fresno, in the case of pictographs). Then for each pair of counties i and j, we can write a 2 by K table showing the number of elements in each category: Category 1 2 K County i n.l n2 n County j nji nj2 nJK Then we define the modified chi-square distance measure from county i to county j, x.., by K 2 2 Xi (:= ::) n + (n;k ni+) k=l n n ik i _ where n =n +n nnn +k ik jk' k i+ E ik' + k=l k k=l n k n = i (n.k + n ++ ~1Z ik jk The chi-square metric is a true distance measure in that x. is close to zero if counties i and j are similar, while xi is large if counAies i and j are very dissimilar ("tfar apart"f). J The indicator metric, w.., is defined in the following manner: ij 9 106 Let 1 ifn = and n =0 ik jk Ijk 1 if n 0 and n c- 0 ijk ik jk 0 otherwise K Then w.. = - I . Clearly, cw* _K. The indicator metric is an inverse ii j ijk i distance measure, as w. =O when counties i and j are similar on no categories (and, hence, are 'ffar aart"), while w = K when counties i and j are similar on all categories (and, hence, are "tcl'oe togethertt). Using one or the other of these formulas we can create an N by N proximity matrix giving the distance from each object to each of the N-1 other objects. Mathematically speaking, these N points will fit exactly in an Euclidean (N-1) dimensional space. Multidimensional scaling is a technique for approxi mating the true configuration of these N points in (N-1) dimensional space by a configuration of N points in a space of lower dimensionality, typically one or two dimensions. The approximating configuration is picked to maximize the goodness-of-fit between the true and approximate configurations. This tech- nique is almost universally applicable for two reasons: (1), no assumptions are made about the underlying distribution of the N objects to be scaled. Many other methods demand that rigorous criteria, such as normality, be satisfied; and (2), multidimensional scaling is nonmetric in nature. All computations are based on the ranks of the distances rather than on the distances themselves. To test the usefulness of this technique, we analyzed petroglyph data for 37 California counties and pictograph data for 23 California counties. The raw data consisted of the total number of recorded occurrences in each of 5 categories (human, animal, circle and dot, angular, and curvilinear) by county, as reported by Heizer and Clewlow, Jr., in Prehistoric Rock Art in California (pp. 69-92). Figure 1 identifies the location of the counties under study. Figures 2-4 depict results for pictographs, while Figures 5-7 show results for petroglyphs. Three different measures of association were computed for both the petroglyph counties and the pictograph counties: (1), the modified chi-square metric based on all 5 categories (K=5) [See Figures 2 and 5]; (2), the modified chi-square metric based only on the angular and curvi- linear categories (K=2) [See Figures 3 and 6]; and (3), the indicator metric, based on the human, animal, and circle and dot categories (K=3) [See Figures 4 and 7]. The first metric is based on all of the available data. The second and third metrics reflect the notion that the first three categories are some- how different from the last two. The first metric, based on all five categories of elements, would be assumed to give the best results, but at the same time some element categories are more strictly defined than others. Circle and Dot and Human are the least variable and most precise classes. The Animal group is generic in the sense that it includes lizards, snakes, deer, bighorn 107 sheep and other life forms. If we assume that the petroglyph authors viewed these different animals as separate, rather than as equal and indistinguishable life forms, then we have imposed upon these distinct glyphs which may have had quite different meanings, a single label which conceals, or at least ignores, that variation which can be presumed the Indians were aware of. Least precise of our broad categories are the Geometric and Curvilinear groups which tend to be catch-all labels for a very wide variety of designs, none which are natural- istic, or at least recognizably so. For these reasons the second and third metrics are applied in order to see if these differences in "classificatory reality" will produce meaningful results. In each application of the chi-square metric, the counties were scaled down to two dimensions (see Figures 2a, 3a, 4a, 5a, 6a, 7a under each main heading) and to one dimension (see Figures 2b, 3b, 4b, 5b, 6b, 7b). When the N counties are scaled down to one dimension, they can be ranked by the value of their one coordinate into a natural ordering from the largest to the small- est. We can then assign the rank of 1 to the county with the largest coordin- ate, 2 to the county with the second largest coordinate, ... , N to the county with the smallest coordinate. Figures 2c, 3c, 5c, 6c show the rankings of the counties superimposed upon their geographical locations. Unfortunately, the scalings based on the chi-square metric do not yield any tight, distinct clustering schemes. The rankings do not appear to reflect geographic distances or geomorphic similarities. The scalings based on the indicator metric do reveal tight, compact clus- ters (Figures 4a,7a). Unfortunately, little, if any, geographic sense can be made of these groupings (Figures 4b, 7b). What conclusions can we draw from this? One possible conclusion is that the distribution of California rock art styles over time was not always along the same geographical lines. One must bear in mind that the results of a multi- dimensional scaling are only as good as the data put into it. One source of difficulty is in the definition of the design element categories. If the categories are well-defined, non-overlapping groupings, then there should be no problems. However, if the categories have been defined so that there is some question over which category a design falls into, then this fact will be reflected in the scalings. This does not appear to be the source of diffi- culty here. The main problem in securing better style distributions using the 5-class design type frequencies may lie either in too few available data, or in the lumping of too many different elements under too broad categories (especially those called Angular and Curvilinear), or in treating, as though they were equivalent, design elements from a wide time range where some ele- ments had floruits of centuries and others perhaps of decades. 108 Examination of the counties which appear to be misplaced indicates that the counties which show the greatest deviation from their expected location are those with the fewest number of elements present. This could be rectified by additional sampling data from those counties, An entire branch of statistics is devoted to problems of sampling, and it is not the purpose of this paper to summarize the current literature in this subject. Nevertheless, a few general comments are called for. Assume that the probability of finding elements in one particular category is quite small. Then we would expect to find zero elements from that category in a small sample, while we would expect to find several elements from that category in a large sample. Such a discrepancy will result in a large apparent distance between the associated counties. In the data under consideration, the rarest category is the circle and dot (2.0% of the pictographs and 2.5% of the petroglyphs). In a sample of 50 pictographs we would expect to find one circle and dot element. Therefore, selecting a sample of at least 50 elements would make the expected number of elements in each category at least one. This is obviously a crude rule-of-thumb--many others could be suggested--nevertheless, it does suggest areas for further research and further study. Analysis of Nevada petroglyph sites might be a logical next step. Heizer and Baumhoff (1962) identified 58 discrete petroglyph symbols or elements and catalogued their occurence at 71 sites in eastern California and Nevada. The Nevada sites display the same variation as those in the California sample in the total number of elements at each site: the smallest site contains only one element, while the largest site contains 705. The average number of ele- ments per Nevada site is considerably higher: 68.89. Unlike the California data those from Nevada data contain, for the most part, a sufficient number of occurences per site. While a detailed analysis might indicate the need of eliminating the very smallest sites from the analysis, this is not a major problem. The success of the analysis lies in a judicious choice of element categories. It is in this area that the inter- face between archaeology and statistics becomes important. 38 out of 58 elements occur fewer than 71 times. Ideally, we should like the expected number of occurences of each element per site to be at least 1. Therefore, we would attempt to aggregate some of the smaller categories by combining similar element types, e.g., combining the "mountain sheep" elements with the "sheep horn" elements to form a major class of element types. The statistician can be useful in suggesting the extent of aggregation required; the archaeologist, on the other hand, must indicate which aggregations make sense from a cultural point of view. Careful aggregation of the data is one of the most important aspects of the analysis. Once this has been accomplished and an appropriate metric chosen (in view of the large number of elements, either the modified chi-square 109 statistic or the product-moment correlation coefficient probably would be a wise choice of metric), the remainder of the analysis would proceed in the manner outlined above. In summary, we have applied the concepts of proximity matrices and multi- dimensional scaling and have shown how they can be applied to one body of archaeological data. While the results are not very revealing, they, neverthe- less hint at the power of the method and suggest areas in which further appli- cation might be beneficial. Center for Advanced Study in the Behavioral Sciences Stanford, California June 15, 1973 110 KEY TO PICTOGRAPH FIGURES = Amador = Fresno = Inyo = Lassen = Mariposa = Mono = Orange = Santa Barbara = Santa Cruz Island = San Luis Obispo = Stanislaus = Tuolumne 2 = CAL 4 = IMP 6 = KER 8 = LAN A = MOD C = NNT E = RIV G = SBR I = SDI K = SIS M = TUL Ca laveras Imperial Kern Los Angeles Modoc Monterey Riverside San Bernardino San Diego Siskiyou Tulare KEY TO PETROGLYPH FIGURES = Amador = Calave = Eldora( = Humbol( = Inyo = Lake ras do dt 2= 4= 6= 8 = A = = E = G = I = K = M = O = Q = S = U = W = Y = Los Angeles Mariposa Mendocino Mono Nevada Placer Riverside Santa Barbara Santa Clara San Nicolas Island Sierra Stanis] Tulare laus BUT CCO FRE IMP KER LAS MAD MER MOD MNT ORA PLU SAC SBR SDI SHA SIS TRI Butte Contra Costa Fresno Imperial Kern Lassen Madera Merced Modoc Monterey Orange Plumas Sacramento San Bernardino San Diego Shasta Siskiyou Trinity 1 3 5 7 9 B D F H J L N AMA FRE INY LAS MRP MNO ORA SBA SCI S LO STA TUO 1 3 5 7 9 B D F H J L N p R T V x z AMA CAL ELD HUM INY LAK LAN MRP MEN MNO NEV PLA RIV SBA SCL SNI S IE STA TUL A _ I Ill CALIFORNlA C'OU'NTY MIAP Abbreviations: Ala, Alanieda: Alp, Alpine; Ania, Amador; But, Buttc; Cal, Calaveras, Col, Colusa; CCo, Contra Costa; DNo, Del Norte; Eld, Eldorado; Fre, Fresno; Gle. Glenin; I luni, Hulinboldt; Iimp, Imperial; Iny, lnyo; Ker, Kern; Kin, Kings; Lak, Lake; Las, Lassen; LAn, Los Angeles; Mad, Madera; Mrp, Mariposa; Men, Mendocino; Mer, Merced; Mod, Modoc; Mno, Mono; Mnt, Moniterey; Nap, Napa; Nev, Nevada; Ora, Orange; Pla, Placer; Plu, Plumas; Riv, Riverside; Sac, Sacramiento; SBn, San Benito; SBr, San Bernardino; SDi, San Diego; SFr, San Francisco; SJo, San Joaquin; SLO, San Luis Obispo; SMa, San Mateo; SBa, Santa Barbara; SCI, Santa Clara; SCr, Santa Cruz; Sha, Shasta; Sie, Sierra; Sis, Siskiyou; Sol, Solano; Son, Sonoma; Sta, Stanislaus; Sut, Sutter; Teh, Tehama; Tri, Trinity; Tul, Tulare; Tuo, Tuolumne; Ven, Ventura; Yol, Yolo; Yub, Yuba. SMa l EGEND Pet rogl yph P ictograph SNi 0-1 SNi ()-1 Both FIg. 1 Cal Ifornia Counties- Included in this Study 112 0 0 ~~~~~~~~~~~~~~~~~~04 I A . * I C * tZ0 _ , .~ 0 . , 100 Z * 6 0 N * *00 g . 0 .S .0 . .. : :8 . * , .o - 0 co00 0 . , . 4 o. ; I;. 0 * , *^ 4 * S 0 4~~~~~~~~~~~~~~~~~~~~~~~4 - * 0 , *00 ~~~~~~ 0100~~~~~~~~~~~~~~~~~~~~- W * , a 0,1 * * . oN40 0 .0 _ * I * r , o _~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~' d,~~ m ,r . VIoefj 0. ' , 0 1 . N * * 4 *~~~~~~~~~~~~~~~~~~~~ *.C * , 5 .0 . , ~~~~~~~~~~.0 .~~~~~~~~~~~~~~~~~~~ , .0 * ,~ . . .oC AL 0 _ * -. 4 . *- - .* ;e * , Q * 5 b~~* 5 _* SW 00 C J 0 **OC . Sn X? * C * ~~~~~I S. L * , 5o ., ,.^V * 4.j1 g* e - * g U) 0.* _ . 4O.1 0 5* C* 0 C . *J ZI CU S < * C .5 .* - g 4. g 0.0@ o. . s Q) .0* 4 x* I n4 E~~~~~~~~~~~~~~ C ,* 4 I- 5 * . . 0 ~o *s ; L; * I~~~~~~~~~~~~~~~~~~~~~0c) *e o l * I 0 _ * 0 *.C | 0O 5.. - * I . .-CS- * . . . ' _. . 1* C~. C-4 0. .* - ?0. * r ' C Z * .4 C4 '0 .fi _ *o^r0 ' 7 Cr4?NQas-0+:C -s-?~OO 0 P.4 s , reCuw,Pe c~~ ~~~~~~~~~~~~~~~ ~ a 4*e*e-es@@@@@@*@*e@@@@@@@ e -* 4 0 0 s^ j^ ______OOOooO tOoCC^*~_-~~~~Nsssf a. I us| | I I | | I 113 IMP STA I NY 'O TU)L FRE SBR KER, Sib CAL SBA SD TUO RIV MNT AMA MNO ISC I LAS LAN OR& Fig. 2h PI CTOGRAPHS Metric is Modified Chi-Square Statistic Based on All Elements 1 nimensional Solution 114 CALIFORNIA COU'NTY NAP 0DNo Sis Mod Abbreviations: Ala, Alameda; Alp, Alpine; Ama, Ainador; Lt i L4 | But, Butte; Cal, Calaveras; Col, Colusa; CCo, Contra Costa; DNo, Del Norte; Eld, Eldorado; Fre, Fresno; Gle. Glenn; i I U ( ---llum, Humboldt; Imp, Imperial; Iny, Inyo; Ker, Kern; Kin, Hum /~~ C Ti sSa a Kings; Lak, Lake; Las, Lassen; LAn, Los Angeles; Mad, Tr i Sha 1Las Madera; Mrp, Mariposa; Men, Mendocino; Mer, Merced; Mod, Modoc; Mno, Mono; Mnt, Monterey; Nap, Napa; Nev, Nevada; Ora, Orange; PJa, Placer; Plu, Plumas; Riv, Riverside; Sac, Sacramento; SBn, San Benito; SBr, San \--J i Teh >/; -, | Bcrnardino; SDi, San Diego; SFr, San Francisco; SJo, San Plu g Joaquin; SLO, San Luis Obispo; SMa, San Mateo; SBa, _W) ' vv ,>. y 1 Santa Barbara; SCI, Santa Clara; SCr, Santa Cruz; Sha, Men ;-. Gle i But ) Sie 1 Shasta; Sie, Sierra; Sis, Siskiyou; Sol, Solano; Son, Sonoma; ( C _ _. y !3.../'\Sta, Stanislaus; Sut, Sutter; Teh, Tehama;Tri,Trinity;Tul, "a /, N --- Tulare; Tuo, Tuolumne; Ven, Ventura; Yol, Yolo; Yub, CoI S Yub I ak Pl.. _1_Yuba. Eld ~' yolS ItL _. ___ . Son A 001. J uo n SFr \C Ala I 'ZN rp/ SMa ~ Sa, s ' SC)1 Mer Al"'4140- / \,>Ri S ~ ~ ~ c Mad 8 Ip _ \~ ' !" iq Fre Iny ~SBrn ". t ~~~~Tul L "'\,/ Kin . ~ ~ ~ ~ 1 . SLO . Ker SBr fin 1 D o SB ~ ~ ~ ~ ~ ~ ~~D P I CTGRPH Met ri c I s Mod i fied Ch i -Squjare Stat ist Ic Based on allI Categ,or ies County Ranking, Def ined by 1 Dimensional Solution 115 * * * * * 0 0 ;* 000 * 00.0*000*0*0900*000*000*.0*0000*0** *00* 00 0*0-00 00* *** Z * * , 0 01 . , .4 Z 4 , * 0 w 0a 7 0 a ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~y0 - 0 ~~~~~~~~~~~~~~I 0z' * , * .00 * a .0 0 g 4 N 0 a @0 . * I *0 'C * 0 . d o 0 , 04 , .c,.o o~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~c .- , . 0 . , 0 4 0 0 0 . ,0. 4 U~~~~~~~~~~~~~~~~~~~~~~~~~~~4 U 44 M . ~~~#4 * g 0 0~~~~~~~~~~~~~~~~~~~- r IL * I *0 * , oNO p. , . o Var 0 * , * 00. U.~ . ri 0 . ,04. er z L 0 0 04 C * a *0 * S 0 ff L ~ ~~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~ * I, _ UL Z o0 aNF I f tN 0 P0 ff-04C M I- C "-v?- -N4c 7 . 0 S .0- t * * SW I W 0 * I .0 ** LX * g 40o p. a 0 . 4 * a *o0 Z * 2 400 _ * I * CO 4 * 5 - of. 0 0 .50 o zr * a .0 C -* G *0* * * .00*e *~~~~~ 0 *.0 >~ 0 cn . 0 Ur o I4 S < * s @ () ........... a ?~~~~~~~ 050 0 I U) . * * Z * . 0 *O 4 * I a .000 0 .-*i i Q) v.14 I! _ . I .g. - vr * 4I 4 .* 3 000 4* z * I|z 00i< - C~~ ~ ~ -Jo I .0 *| _C _.- I0.* ) 0) ?f _ *0 . 0 0_* Fn -o * O p * - -. C0I.--4-,-I *.4 ... * ! *Xo c To I 001 p . ,o .,.00 , 7f * , CJ0; . U ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~4L. Cs * * ) * 4 I* S k44' m * ci *. , o^ o o- r 0 t C * tN 0 . r s ne_f@+~ta 4. 0f+N 2eP l F^ tkSt *04 {)_C 1ke Jd ,> z. * . 0 0@eeeeee@@@@@@eee C_. 4 0 0 OOOOO?OOOOOOOOOC~ _ | @ 1 | @ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 H I0 l F - ORA r - LAN LAS I - MNT ScI RIV TUO SDI ,--- MRP SBA KER MNO SLO TUL 6BR CAL MOD FRE STA Fig. 3h P ICTnGRAPHS Metric is Modified Chi-Square Statistic Based on Angular and Curvil inear Elements 1 Dimensional Solution 116 I I I I I 0 117 CALIFORNIA COUNTY MAP Abbreviations: Ala, Alameda; Alp, Alpine; Ama, Amador; But, Butte; Cal, Calavcras; Col, Colusa; CCo, Contra Costa; DNo, Dcl Norte; Eld, Eldorado; Fre, Fresno; Gle. Glenn; I unm, Humboldt; Imp, Iniperial; Iny, Inyo; Ker, Kern; Kin, Kings; Lak, Lake; Las, Lassen- LAn, Los Angeles; Mad, Madera; Mrp, Mariposa; Men, Mendocino; Mer, Merced; Mod, Modoc; Mno, Mono; Mnt, Monterey; Nap, Napa; Nev, Nevada; Ora, Orange; Pla, Placer; Plu, Plumas; Riv, Riverside; Sac, Sacramento; SBn, San Benito; SBr, San Bernardino; SDi, San Diego; SFr, San Francisco; SJo, San Joaquin; SLO, San Luis Obispo; SMa, San Mateo; SBa, Santa Barbara; SCI, Santa Clara; SCr, Santa Cruz; Sha, Shasta; Sie, Sierra; Sis, Siskiyou; Sol, Solano; Son, Sonoma; Sta, Stanislaus; Sut, Sutter; Teh, Tehama; Tri, Trinity; Tul, Tulare; Tuo, Tuolumne; Ven, Ventura; Yol, Yolo; Yub, Yuba. SMa Iny 7 SBr b go S9 SNi 0-1 Riv SDi is Imp I Fig. 3c P I CTOGRAPHS Metric Is Modified Chi-Square Statistic Based on Angular and Curvilinear Elements County Rank ing Def Ined by 1 Dimens ional Sol ut ion 9 S Li 6 Ker I 118 ~~* * * * * ... 0 0 0 0 0 0* 0 000*0 0 0* 0 000 0 000 00a00* 0 f ~ * , * . Z * , 0.0 C * , Z * , * . L 0 C *- * I 0o *~~~~ 9 * 0o 0 *, 9 i * 0 . @ x t . rC C 0 '~~~~~~~~~~~~~~~~~~~~~~~~~m o . * ? * r 0 0~~ ~ ~ 0 b." 0*^ 0 - j 9 * .a O' 0 I hI -o **N o * 000 * 1o 00 0 *& ,I ,Z j . t @ J < X g g Z~~~~~~~IJ Q * Z hI *@tUW | # FU) IC *S I * r 0 I * 0 cr ee -i CL bi j a g I Pz g 0jU 0r * C * C4 0 I _*i C _n * I * O -J00J. ii>~~~~~~~~~~~~~~~~4 i4 C s ; 0 0 * C _. *. 0 = ? m s u v . 4t,~~~IW*1,, WWt 0 1" a0". i. uf * OW > g I I -)t^? Cax 0O* S n . "''a E ' ' E < a WU cOW. - 8- >* _ % S %* 0 *F c O .wo .~~~~~~~~*W I o~~ Q) 40 0.0 C -3 *4 -4 IC I - -1 C . Lf X . hII h I. eF~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C a @C" hIJ r -1 Ws .0 e C.; * I! .! ^ *4i - 0.0 _ 5-c c I*n _ . 0 * C _. 9 * HEr-( 0 _ * * |L ' ~ . * 0 : c~~~~~~~~~~~~~~~~~~~~~~ .0 . z 0. 0 so .<. ... ... .. 0 . .. .... . 0 ... . .... 0 ... . .... 0 ... ..... 0 ... .... . * . .. ..... * .......*.. .....*..... (: * *C *0 ; C, i - ~JO C 1 t _ . . 1O4 UN - CC N -I uo r x O Ix C + 7 LC U C, 1T .. C _n 't r, C t (- -4 cc C t - _ -4 C), ?-- Lr * - 4 C - ^ C Z ;1 O . r N r N _ r Jr x. C u V ) O- e. r : t- ' 'P P- M C- -0 0 0 - - 0 0 * 0 9 9 0 * 0 0 0 0 0 0 0 0 0 0 0 ' e n CO _ N e 0. * 119 CALIFORNIA COUNTY MAP Abbreviations: Ala, Alameda; Alp, Alpine; Ama, Amador; But, Butte; Cal, Calaveras; Col, Colusa; CCo, Contra Costa; DNo, Del Norte; Eld, Eldorado; Fre, Fresno; Gle, Glenn; Hum, Humboldt; Imp, Imperial; Iny, Inyo; Ker, Kern; Kin, Kings; Lak, Lake; Las, Lassen; LAn, Los Angeles; Mad, Madera; Mrp, Mariposa; Men, Mendocino; Mer, Merced; Mod, Modoc; Mno, Mono; Mnt, Monterey; Nap, Napa; Nev, Nevada; Ora, Orange; Pla, Placer; Plu, Plumas; Riv, Riverside; Sac, Sacramento; SBn, San Benito; SBr, San Bernardino; SDi, San Diego; SFr, San Francisco; SJo, San Joaquin; SLO, San Luis Obispo; SMa, San Mateo; SBa, Santa Barbara; SCI, Santa Clara; SCr, Santa Cruz; Sha, Shasta; Sie, Sierra; Sis, Siskiyou; Sol, Solano; Son, Sonoma; Sta, Stanislaus; Sut, Sutter; Teh, Tehama; Tn, Trinity; Tul, Tulare; Tuo, Tuolumne; Ven, Ventura; Yol, Yolo; Yub, Yuba. AI SMa Kin Human Elementsl Absent;Circle & Dot Elements Present Human Elements Pre- sent; Circle & Dot Elements Present Ven Human Elements Present, i O Circle & Dot Elements Abse9nt 1 Human Elements Absent; Circle & Dot Elements Absent MAP 2. LEGEND .\ Fig. 4b P I CTOGRAPHS Metric is Indicator Function on Human, Animal, and Circle and Dot Elements Counties are Classified According to 4 Main Groupings from 2-Dimensional Solution --4 I 120 ........: S :e e..:.:. *~~~~~~4D IFe to~~~~~*.e *e * 0 ..0 to* t f es e*.ee@ toO 2 * . a . , Is4 o . - * , . m o . , . mo * , .o 9.. .' , .O v , 5 .M . a- 0 a0 * S S0 o * * 4 * I Oe * . e F * e 4 * * em Wa 44 I 0 * *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~r ? * * *NO 4) ~ : * * 0.. * 5 *4 * I .@4 ; I @4 L. v ,._ * et * , . m *II . m I 4, . - O.-* 6 6 0.CO . ' *N - , .o * , .o * , 0e. * , . 4 , . 4 * , :. ** , .eM S, . O~ ~ ~ 9 * 0. a.'~~~ * S *. 0 _ ,.,. . ,,,- o **** <* d* *e ... * * *-* * *** *,-...v. ..0.4. ....*.. *-*,* *... .. *,. a< . I * C f w 0. * . I .6 * .Q 4 4 . o~ ~ S _ ..o C, ,. , n 1. 4 . 4 V* ._ o -: tU a,v g: S z . s2Q| .i4r - . U t . , . X ,.. , ^ 7 * 4 'a s -: I .x .me., a z . * 0n L _ ** I00 e~ 00 0 04 0 0 eee Oo e .' ..* *, U t ON .5A * | C)* _ * @~ ??* ? 9 @ * .*o U) *@X C S.ls Ise il .ll 055 121 | - I NY t PLA MRP 4 - LAP _,_ NEV -MER CAL SHA SBR mot) ELD KER R I V Kp- SIE SD I ORA PLU FRE S's MNT HUM TTA Cco A C1ns1rBUT SCL TUL .LAK ,tAD SBA SNI LAN Fig. 5h PETROGLYPHS Metric is tModified ChM-Snuare Statistic Based on all Elements 1 Dimensional Solution 122 CALIFORNIA COUNT'Y MAP Abbreviations: Ala, Alaineda; Alp, Alpine; Ama, Amador; But, Butte; Cal, Calaveras; Col, Colusa; CCo, Contra Costa; DNo, Del Norte; Eld, Eldorado; Fre, Fresno; Gle, Glerin; }lum, Humboldt; Imiip, Imperial; Iny, Inyo; Ker, Kern; Kin, Kings; Lak, Lake; Las, Lassen; LAn, Los Angeles; Mad, Madera; Mrp, Mariposa; Men, Mendocino; Mer, Merced; Mod, Modoc; Mno, Mono; Mnt, Montcrey; Nap, Napa; Nev, Nevada; Ora, Orange; Pla, Placer; Plu, Plumas; Riv, Riverside; Sac, Sacramento; SBn, San Benito-; SBr, San Bernardino; SDi, San Diego; SFr, San Francisc;), SJo, San Joaquin; SLO, San Luis Obispo; SMa, San Mateo; SBa, Santa Barbara; SCI, Santa Clara; SCr, Santa Cruz; Sha, Shasta; Sie, Sierra; Sis, Siskiyou; Sol, Solano; Son, Sonoma; Sta, Stanislaus; Sut, Sutter; Teh, Tehama; Tri, Trinity; Tul, Tulare; Tuo, Tuolumne; Ven, Ventura; Yol, Yolo; Yub, Yuba. SMa Iny 37 b Ker SBr 24 28 SNi 0-1 2. 25 Riv SDi 20 Imp 21 Fig. 5c PETROGLYPHS Metric Is Modified Chl-Square Statistic Based on Al l Elements County Ranking Defined by 1 Dimensional Solution Sis 27 29 123 0~~~~~~~ * , * . z 0 * 0 0 .0 0 00 0 0 0 *0 0 *. 0* . 0 . 0 00 0 * 0 0 Cn . *0 _L . gX 7 0. 0 o Uj * , 0 0 4 o . , 0 04 o . .0^ * * , .0. p.. * , *0 4 * . S 0 4.. o . , . 4 o . , . 4 * , * 00. V, , .04 V4 . , .04 UJ * , -*.0 * . . . No 0 . , . 0 5 0~~~~~~~~~~~~~~~~~~~~~~0 *~~ S .S 0 , 04. 5 0 , > . .0 Ca * a *o0 * - ' . U . . C . , .0_ 4. * *0 Z. ~~~~ 0 I ~~~~~~~~~~~~~~n0~ 4 . ,I 0 4 3 . ,. Z * , 00e _ * * *0 I -J 0 a .......... OCC _ * a * 0 * * C! U * a * 0 Zi * 5 * .0 U. .0' J * 1 "* I *0 _ .$ 4 2 o a ~~~~ 0 04 41 .,..~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~, 0. ' - -; O* I.0 R S C a -- o~ 0* '* . I I :,~ .0D * * 4C v~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~l co zS -Z - * I g *-1 Q Ur * rv 4 * I4.)s Ae ,< ; {_4 I -. * Cl . r d 4 '- I j3 oo o 0' o U . , ?3 n 0O o u* ' tn *. an J0 * | ., '- . I - S * I ,-4 v- .Oa -L 0 a v44k L No*I C. *. ) an * IvI 0 / * { vF -* I , C * I * . .O r4 ~ ~ ~ 6 an ? I f EFsN+4aeZZ~ar^Nc0{ '~~~~~~~~~~~~ 0 .0~~~~~~~~~~~~~~~~~00 0 r - e 0< N _ a V% U, f P -4D t tr _' o% ? 0 U- -t ~- O NZ C _ -t oy C' P-~ c 0?oo z ' - 4 - N _ o Pb v r IN 4 o P o k C _ . It Ml _0 a, - N C C a) m an N ? W% C 0 C O * . U*)*@********.**- *- Z -" 'o 't CC ID - ey fe -t of-- -- co o' C C% OD O. 'c C% - B -- - N NNNN U, 0-. 0~~~~~~~~~~~~00 QA -.0 -I.' *U C; ' 124 SBA l , ELD PLA MER SAC ___, __ MU_ I NY ' ~~~~~~tR ORA TU- ,r CAL IMP K ERP l~~~~~ I FRE PLU MOD $1 LAN TR I MNT STA LWU MEN 4 _C~CO < , bUT SCL , , MAD SN I LAK Fig. 6b PETRO(.LY PHS Mletric Is Modifted ChI,Sq9are Sta istic Based on Angular and Curvilinear Elements 1 nImensional Solution 125 CALIFORNIA COUN'IY MIAP I Abbreviations: Ala, Alameda; Alp, Alpine; Ama, Amador; a But, Buttc; Cal, Calaveras; Col, Colusa; CCo, Contra Costa; DNo, Del Norte; Eld, Eldorado; Fre, Fresno; Gle. Glenn; I llurnl, liu:niboldt; Ii'p, liperial; lIy, lnyo; Ker, Kern; Kin, Kings; Lak, Lake; Las, Lassen; LAn, Los Angeles; Mad, Madera; Mrp, Mariposa. Men, Mendocino; Mer, Merced; Mod, Modoc; Mno, Mono; Mnt, Moniterey; Nap, Napa; Nev, Nevada; Ora, Orange; Pla, Placer; Plu, Plumas; Riv, Riverside; Sac, Sacramento; SBn, San Benito; SBr, San Bcrnardino; SDi, San Diego; SFr, San Francisco; SJo, San Joaquin; SLO, San Luis Obispo; SMa, San Mateo; SBa, Santa Barbara; SCI, Santa Clara; SCr, Santa Cruz; Sha, i | Shasta; Sie, Sierra; Sis, Siskiyou; Sol, Solano; Son, Sonoma; 4l Sta, Stanislaus; Sut, Sutter; Teh, Tehama; Tri, Trinity; Tul, Tulare; Tuo, Tuolumne; Ven, Ventura; Yol, Yolo; Yub, .i Yuba. SMa SBr Ld* 2lc S>tN 0V_ 2. dVSNi 0-1 Riv SDi 19 Imp 2-1 15 Las 19 - Fig. 6c PETROGLYPHS Metric is Modified Cht ,Square Statistic Based on Angular and Curvilinear Elements County Ranking Defined by 1 Dimensional Solution 126 60 * 0*@* *****-***.0* * * * * * . * . * * ' * 6@ LQ * 6fl 0 .41 x * r | . _ ,,~~~~~~~~Z . 0^ o * s.? !f . ; 41 0 ~~~~~~~~~~~~~~~A0 6-.J *0 O~~~~~~~~~~~~~~~~~~~~0 oc IL l * 6- 9 _* ,0 o * . * |I * 6 z Z * 9 66 U * * SMI .0 * 6' * z - g 0'r,g; wc * 9n .0 X* r M * 0, 9jfi-;; L 1 * 0z * AI s . 0 0 O '. *6 J4 C - 0 * .000| %4 $ x 4 . 0 ,cd ~J x 0. Wee^s _ , * 1 * 6< Z 1- C * 0 o _ * I * O 00 ***@*******. * *~ 0 z . ork*jvN@co_*a - i n . - o. ' Ix K S' rI 0* q -j 4 10 04~~9 i o0 0.2CC Fz.iE-I'~~r4 -r4C1 0 * % l~~,~* 0 U. C~~~~~~~~~~~~~~~~~~~0 60. 6- U, C- C~~~~~ C''C C I~~~~~~~~~~~~~~~~~~I 127 CALIFORNIA COUNTY MAP Teh Gle Col Ss Y, Son ~ap~ Ala s a Abbreviations: Ala, Alameda; Alp, Alpine; Ama, Amnador; But, Butte; Cal, Calaveras; Col, Colusa; CCo, Contra Costa; DNo, Del Norte; Eld, Eldorado; Fre, Fresno; Gle. Glenn; hlunm, Humboldt; Imp, Imperial; Iny, lnyo; Ker, Kcrn; Kin, Kings; Lak, Lake; Las, Lassen; LAn, Los Angeles; Mad, Madera; Mrp, Mariposa; Men, Mendocino; Mer, Merced; Mod, Modoc; Mno, Mono; Mnt, Monterey; Nap, Napa; Nev, Nevada; Ora, Orange; Pla, Placer; Plu, Plumas; Riv, Riverside; Sac, Sacramento; SBn, San Benito; SBr, San Bcrnardino; SDi, San Diego; SFr, San Francisco; SJo, San Joaquin; SLO, San Luis Obispo; SMa, San Mateo; SBa, Santa Barbara; SCI, Santa Clara; SCr, Santa Cruz; Sha, Shasta; Sie, Sierra; Sis, Siskiyou; Sol, Solano; Son, Sonoma; Sta, Stanislaus; Sut, Sutter; Teh, Tehama; Tri, Trinity; Tul, Tulare; Tuo, Tuolumne; Ven, Ventura; Yol, Yolo; Yub, Yuba. N :d^; All . ?ITuo Jo SBn Kin HIuman Elementsv Present; Anirmal Elements Absent Human Elements Pres sent; Animal Elemeni Present Human Elements Absent; Animal Elements Present :*o Human Elements Absent; Animal Elements Absent LEGEND Ill lilII 1 ,W1 iii 'IJVJA. Ven 4b _ ' 0 IT t fn I erd 1 U(- FIg. 7b PETROGLY PHS Mletric is Indicator Function on Human, Animal, and Circle and Dot Elements Countles are Classified According to 4 MlaIn G:roupinng from; 2-Dimensional Solution I I I I;I I r 128 4~~~ ~ ~ r l flI 2 ? s.> > i, ws -\;, -----I MAP OF PETROGLYPH SITES WITH STYLE AREAS OUrLINED 4 ! '' * \; * )\ ~~~~~~~~~~~~~(Each dot represents one site) ~~~~~~~~~~~~~~~GetBsnStyle \t/ , 1 I23' I22 I2|- I20 I89' @6' II7- ;$' IiS ... ,. , ..... , 5 . . Fig. 8* California Petroglyph Style Areas (From Heizer and Clewlow 1973:Map 15) 129 t', t. at. I. I Z@ 0 g 7 123__ 122 1Z 20' 117' )LJi f . - --Northeast Painted Style C" ' J3 j MAP OF PICTOGRAPH SITES -'S @ , \ i (Each dot repri It - -.._ ,/Z' ) ( W , ,- " -s !. C L I II." 115- *. Am -42 ; WITH STYLE AREAS OUTLINED 41a ,esents one site) -40' -39m Southern Sierra - Style South Coast N Range Style Santa Barbara Style Southwest Coast Style 123' 122' 120' lIe' 11 7 Fig. 9. California Pictograph Style Areas (From Heizer and Clewlow 1973:Map 16). s8i Yr 36 35"- -3' -36 33 -3S miclle I IA I p I 0 10 a hp I ? 0 r r 1 .41 121 III;C 130 BIBLIOGRAPHY Heizer, R. F. 1973 Heizer, R. F. 1962 and C. W. Clewlow Prehistoric Rock Art Ramona, California. and M. A. Baumhoff Prehistoric Rock Art of California Press. of California. 2 Vols. Ballena Press, of Nevada and Eastern California. University Kendall, M. G. and A. Stuart. 1959 The Advanced Theory of Statistics. C. Griffin and Co., London. Lorandi di Gieco, A. M. 1965 Sobre la aplicacion de metodos estadisticos al estudio del arte rupestre. Universidad Nacional de Cuyo, Facultad de Filosofia y Letras, Anales de Arqueologia y Ethnologia 20:7-26. Mendoza, Argentina. Maggs, T. M. 1967 A Quantitative Analysis of the Rock Art from a Sample Area in the Western Cape. South African Journal of Science 63:100-104. von Werlhof, J. 1965 Rock Art of Owens Valley, California. Archaeological Survey, Report No. 65. University of California Berkeley.