Fractal Geometry

The main goal of this paper is to provide a generalized definition of fractal dimension for any space equipped with a fractal structure. This novel theory generalizes the classical box-counting dimension theory on the more general context of GF-spaces.
In this way, if we select the so-called natural fractal structure on any Euclidean space, then the box-counting dimension becomes just a particular case. This idea allows to consider a wide range of fractal structures to calculate the effective fractal dimension for any subset of this space. Unlike it happens with the classical theory of fractal dimension, the new definitions we provide may be calculated in contexts where the box-counting one can have no sense or cannot be calculated. Nevertheless, the new models can be computed for any space admitting a fractal structure, just
as easy as the box-counting dimension in empirical applications.

Measuring urban sprawl is a controversial topic among scholars who investigate the urban landscape. This study attempts to measure sprawl from a landscape perspective. The measures and indices used derive from various research disciplines, such as urban research, ecological research, and fractal geometry. The examination was based on an urban land-use survey performed in 78 urban settlements in Israel over the course of 15 years. Measures of sprawl were calculated at each settlement and then weighted into one integrated sprawl index through factor analysis, thus enabling a description of sprawl rates and their dynamics during a time period of two decades. The results reveal that urban sprawl is a multidimensional phenomenon that is better quantified by various measures.

The fractal geometry is introduced in the dynamic fracture to describe the ruggedness
during the crack propagation characterizing the morphology of generated surfaces. It is shown that
the fractal dimension has a strong influence about the limit speed of fast crack propagation. It is also
shown that the inatingibility of speed of waves Rayleigh by cracks in some materials can be
correlated to the ruggedness of fracture surfaces by means of exponent Hurst, H, that measures the
ruggedness dimension. The experimental results of Fineberg et al [FINEBERG 1991; FINEBERG
1992] they were adjusted by the model. The unstability coefficient was calculated for Fineberg et al
measurements in agreement with the definition proposed by SANDER [1984]. One concluded that
exist an intrinsic unstability to the phenomenon that produces the ruggedness of surfaces, limiting
this way the maximum of crack propagation speed for a smaller value than the speed of waves
Rayleigh in the material.

Given the inverse of the Golden Mean $ \tau^{ -1} = \phi  = { 1\over 2} (\sqrt 5  - 1)$, 
it is known that the continuous fraction expansion of $ \phi^{ -1} = 1 + \phi = \tau$ is  $ ( 1, 1, 1, \cdots )$.  Integer solutions
for the pairs of numbers $ ( d_i, n_i ), i = 1, 2, 3, \cdots $ are found obeying the equation
$ ( 1 + \phi)^n = d + \phi^n$.  The latter equation was inspired from El Naschie's formulation
of fractal Cantorian space time $ {\cal E}_\infty$,  and such that it furnishes the continuous fraction expansion of $  ( 1 + \phi )^n ~= ~  (d, d, d, d, \cdots  )$, generalizing the original expression for the Golden mean.    Hardy showed that is possible to demonstrate nonlocality without using Bell inequalities for two particles prepared in $nonmaximally$ entangled states.  The maximal probability of obtaining his nonlocality proof was found to be precisely $\phi^5$.  Zheng showed that three-particle nonmaximally entangled states revealed quantum nonlocality without using inequalities, and the maximal probability of obtaining the nonlocality proof was found to be $ 0.25 \sim \phi^3 = 0.236$.  Given that the two-parameter $ p, q$ quantum-calculus deformations of the integers $ [ n ]_{ p, q}  = F_n $  $coincide$ precisely with the Fibonacci numbers, as a result of Binet's formula when
$ p = ( 1 + \phi) = \tau,  q  =  - \phi =  - \tau^{ -1} $,  we explore further the implications of these results in the quantum entanglement of two-particle spin-$s$ states.

Horton's hierarchical and fractal analysis of channel circumference reveals that tidal-channel systems in the Dutch Wadden Sea have similar branching patterns. Channel systems have the same characteristics as three- to four-times branching networks. The branch lengths of these channels decrease logarithmically. The channel systems can be regarded as ‘statistical self-similar fractal’ networks, considering the natural variability in branch lengths and channel positions. Branching of channels does not continue below the 500 m scale. The channel-system circumference length is logarithmically related to the tidal prism and drainage area. The similarity of the channel systems, regardless of their size, relative amount of intertidal flats, and tidal amplitude, points to a self-organising nature. All processes depend on the feedback between morphology and hydrodynamics. At first sight, the channel systems can be regarded as an ebb-driven drainage network, governed by erosion. However, flood-dominated net sedimentation occurs in large parts of the drainage basins and modifies the ebb-driven network. The complex interaction of hydrodynamic and morphodynamic processes in tidal basins limits the applicability of process-based models. Behaviour-oriented modelling has a wide applicability and can be improved using the fractal geometry as the dynamical equilibrium morphology. The fractal-network geometry can also be used for stochastic reconstructions of fossil tidal-channel systems, when only limited observations are available.

It has been known for a century that small particles dispersed in liquids and gases can form aggregates with extraordinarily low densities, and a variety of studies in the 1960s and 1970s, based on conceptual models and computer models, suggested that “anomalous” scaling relationships were associated with the structures of these aggregates. However, the lack of a suitable theoretical framework and the limits of computer technology inhibited the development of a coherent understanding of the structures of these aggregates and the kinetics of their formation. In the 1980s, the popularization of fractal geometry and rapid advances in computer technology removed these barriers to progress. In this review, the early work on fractal aggregates is discussed and the basic particle-cluster and cluster-cluster aggregation models introduced in the 1980s are described. During the 1990s, interest has been focused on the subtle relationships between aggregation, gelation and spinodal decomposition and on the physical behavior of systems containing fractal aggregates. The following papers in this special issue of the Journal of Sol-Gel Science and Technology on “Computer simulations of aggregation and sol-gel processes” describe recent advances in these directions. They are previewed in this introductory contribution.

هدف هذا البحث إلى دراسة فاعلية تدريس وحدة لهندسة الفراكتال باستخدام الكمبيوتر في تنمية التحصيل, وبعض مهارات التفكير التخيلي لدى طلاب الصف الأول الثانوي.

وقد قام الباحث بتحديد أساسيات هندسة الفراكتال التي تناسب مستوى طلاب الصف الأول الثانوي, وتحديد مهارات التفكير التخيلي المناسبة لهؤلاء الطلاب والتي يمكن تنميتها من خلال دراسة أساسيات هندسة الفراكتال التي تم تحديدها, ثم قام ببناء الوحدة المقترحة في هندسة الفراكتال وتحكيمها, وقد تضمنت الوحدة أحدى عشر درساً وقد قام الباحث بتدريسها باستخدام الكمبيوتر من خلال برنامجي((PowerPoint,GSP, كما قام بإعداد أدوات القياس والتي تضمنت: اختبار تحصيلي في محتوى الوحدة, وأيضاً أعد مقياس لمهارات التفكير التخيلي في المهارات الآتية:( التصور, التجربة الذهنية, تكوين وتوسيع الأنماط), وتم التحقق من صدق وثبات هذه الأدوات.

وقد تكونت عينة البحث من (27) طالباً من طلاب الصف الأول الثانوي بمدرسة الوحدة الثانوية للبنين بمملكة البحرين, واتبع الباحث منهج التجربة الواحدة من خلال تطبيق أدوات القياس قبلياً على عينة البحث ثم تدريس الوحدة المقترحة لهم ثم تطبيق أدوات القياس بعدياً على نفس العينة, وبتجميع البيانات وتطبيق المعالجات الإحصائية المناسبة توصل الباحث إلى النتائج الآتية:

1) يوجد فرق ذو دلالة إحصائية عند مستوى(0.01) بين متوسطي درجات الطلاب عينة البحث في الاختبار التحصيلي قبل تدريس الوحدة المقترحة وبعده لصالح التطبيق البعدي. وهذا يؤكد فاعلية تدريس الوحدة المقترحة في هندسة الفراكتال باستخدام الكمبيوتر في تنمية التحصيل لدى الطلاب.

2) يوجد فرق ذو دلالة إحصائية عند مستوى(0.01) بين متوسطي درجات الطلاب عينة البحث في مهارة التصور لمقياس مهارات التفكير التخيلي قبل تدريس الوحدة المقترحة وبعده لصالح التطبيق البعدي. وهذا يؤكد فاعلية تدريس الوحدة المقترحة في هندسة الفراكتال باستخدام الكمبيوتر في تنمية مهارة التصور لدى الطلاب.

3) يوجد فرق ذو دلالة إحصائية عند مستوى(0.01) بين متوسطي درجات الطلاب عينة البحث في مهارة التجربة الذهنية لمقياس مهارات التفكير التخيلي قبل تدريس الوحدة المقترحة وبعده لصالح التطبيق البعدي. وهذا يؤكد فاعلية تدريس الوحدة المقترحة في هندسة الفراكتال باستخدام الكمبيوتر في تنمية مهارة التجربة الذهنية لدى الطلاب.

4) يوجد فرق ذو دلالة إحصائية عند مستوى(0.01) بين متوسطي درجات الطلاب عينة البحث في مهارة تكوين وتوسيع الأنماط لمقياس مهارات التفكير التخيلي قبل تدريس الوحدة المقترحة وبعده لصالح التطبيق البعدي. وهذا يؤكد فاعلية تدريس الوحدة المقترحة في هندسة الفراكتال باستخدام الكمبيوتر في تنمية مهارة تكوين وتوسيع الأنماط لدى الطلاب.

5) يوجد فرق ذو دلالة إحصائية عند مستوى(0.01) بين متوسطي درجات الطلاب عينة البحث في مقياس مهارات التفكير التخيلي قبل تدريس الوحدة المقترحة وبعده لصالح التطبيق البعدي. وهذا يؤكد فاعلية تدريس الوحدة المقترحة في هندسة الفراكتال باستخدام الكمبيوتر في تنمية التفكير التخيلي لدى الطلاب.

The visual complexity in the temple forms of Pallava Architecture is mainly created by repetition of architectural elements in the Vimana. The elements like Sala and Kuta are repeated in an orderly way in diminishing scale in the vimana. In the south indian temple architecture (Dravidian Style) the super structure of the vimana or its several storeys are set with small temple shapes, Similar to the original shape. The smaller shapes are aligned in a definite pattern at each horizontal level, the repetition of these shapes at each band forming a kind of garland at each level. The repetition of identical shapes either in the vertical or in the horizontal or vertically as well as horizontally, is another frequently used procedure to add visual complexity to the temple form.The article mainly focuses on self similar iteration, repetition, fractalization and how it is applied to various examples starting from monolithic shrines , Shore temple at Mamallapuram to Kailashanathar and Vaikunda Permual temple in Kanchipuram.

The Golden Ratio(aka “golden mean”, “golden section” or “divine section”: standardly denoted with the capital Greek letter Phi) is the only positive (irrational) quadratic solution of the (minimal polynomial) x^2-x-1=0 equation, so that: Phi=[sqrt(5)+1]/2.
The purpose of this paper is to demonstrate some aspects recently discovered by the author of this paper:
(0) a recursive geometrical method for constructing  Phi (inspired from the Taoist religious iconography), which is more simple and elegant than Odom’s method;
(1) an occurrence of Phi  in the water molecule geometry;
(2) a quasi-Pythagorean property of the (Phi,e,PI)  triad;
(3) some other interesting quasi-exact relations between the elements of the (Phi,e,PI) triad;
(4) the tendency of the human systolic/diastolic blood pressure ratio to stabilize to a value close to  Phi with age

Keywords: Golden Ratio/section/mean (Phi), Odom’s method, Taoist religious iconography, water molecule geometry, quasi-Pythagorean property, human blood pressure

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This research has been conducted after studying literature on Environmental Psychology and its role in architecture. This research paper consists of experiments that were carried out to find out the preference of people in shapes and sizes of spaces.

جهانی که در آن زندگی می‌کنیم، سرشار است از اشکال پیچیده‌ای که با قوانین هندسه اقلیدسی نمی‌توان آن‌ها را توصیف کرد. سلول‌های بدن‌مان، سیستم گردش خون، درختان، کوه‌ها، ابرها، رودها و تمامی آنچه طبیعت نامیده‌ایم، به زبان ریاضیات زیبایی به نام ریاضیات فراکتال با ما سخن می‌گوید. بسیاری از تصاویری که در دنیای فن‌آوری اطلاعات ذخیره، منتقل و بازیابی می‌کنیم نیز مربوط به همین دنیای پیچیده و منظم هستند. با توجه به ماهیت خودمتشابهی در ساختار طبیعت، استخراج الگوهای هندسی تکرار‌شونده در اشکال و ذخیره‌ آنها در روش‌های برداری تکرار‌شونده، می‌تواند کارایی بسیار بالاتری نسبت به روش‌های پیکسلی معمولی داشته‌باشد. انگیزه این مطالعه آشنایی با روش‌های عملیاتی‌تر کردن این نوع کدگذاری تصویر و طرح پرسش‌های جدید در این زمینه است. در این راستا، سعی خواهیم‌کرد، با شناخت بیشتر هندسه فراکتالی و مبانی ریاضی استفاده از آن در کدگذاری تصاویر به‌صورت مجموعه‌ای از نگاشت‌ها در زیرتصاویر خودمتشابه، ویژگی‌های عملیاتی این روش فشرده‌سازی جالب و معایب آن در انتقال ویدئو بر روی شبکه‌ را بیان کنیم.

The Fractal Geometry of Life belongs to the new science known as fractology. It is linked to the ancient Greek understanding that gravity is a non-mechanistic colour conscious element evolving consciousness to infinity. Very few people, including most eminent scientists, realise that Isaac Newton, in his 28th Query Discussions, rejected his earlier conviction that the mass of objects in space caused gravity. The movement of Newton’s biologically visible white-light colour particle forms rotating electromagnetically anticlockwise became associated with gravity evolving consciousness to infinity. This was equal and opposite to Einstein’s gravity particles rotating clockwise. The professor of neuropsychology, Richard Gregory, in his paper, Alchemy of Matter and of Mind, published in the journal, Nature, about the Act of Creation, stated that Newton’s book The Vegetation of Metals "proclaimed Newton’s conviction [that the understanding of gravity] had to be completed by a more profound natural science which probed the active principles behind particles in motion.”

El Templo de la Sagrada Familia es considerado construcción no gótica. Esta negación, en parte, es debida por el conocido
hecho de que la distribución de fuerzas, en el Gótico, queda contrarrestada estructuralmente con elementos de apoyo
laterales. Sin embargo, en el Templo la distribución de fuerzas se contrarresta estructuralmente «de manera orgánica»;
o sea, se neutraliza con la construcción de superficies cuádricas que de manera natural genera tal distribución. Sin negar
lo anterior, aquí, con técnicas de Geometría fractal, descriptiva y computacional, aplicadas a las proyecciones básicas del
proyecto del Templo, parametrizamos la característica consistente en la efectividad de ocupar espacio, la escabrosidad de sus elementos. Concluiremos que tal característica sí es gótica, con semejanza general a las catedrales góticas, y en especial con las catedrales de Burgos, París, Amiens y Chartres.

This article argues that any ecological finance theory devised to fit the Sustainable Development Goals (SDGs) needs a paradigm shift in the morphology of randomness underlying financial risk modelling, by integrating the characteristics of "nature" and sustainability into the modelling carried out. It extends the common diagnosis of the 2008 financial crisis with considerations on the morphology of randomness and the reasons why neoclassical finance theory is not sustainable from this perspective. It argues that the main problem with unsustainable neoclassical finance risk modelling is its underlying morphology of randomness that creates a dangerous risk culture. It presents Leibniz's principle of continuity and Quetelet's theory of average as cornerstones of classical risk culture in finance, acting as a mental model for financial experts and practitioners. It links the notion of sustainability with the morphology of randomness and presents a possible alternative approach to financial risk modelling defined by rough randomness. If morphology of randomness in nature is properly described by fractal and multifractal methods, hence ecological finance theory has to include fractal properties into financial risk models. The conclusion proposes a new agenda for future research.

In this paper, we provide the first known overall algorithm to calculate the Hausdorff dimension of any compact Euclidean subset. This novel approach is based on both a new discrete
model of fractal dimension for a fractal structure which considers finite coverings and a theoretical result that the authors contributed previously in [14]. This new procedure combines
fractal techniques with tools from Machine Learning Theory. In particular, we use a support vector machine to decide the value of the Hausdorff dimension. In addition to that, we artifi-
cially generate a wide collection of examples that allows us to train our algorithm and to test its performance by external proof. Some analyses about the accuracy of this approach are also provided.

This webpage explores fractal aspects of Hindu temple architecture, examining multiple archetypes and geometry of recursion. It is primarily about architectural design, religious symbolism and imagination. It concerns religious imagination involved in some of the ideas and plans used in Hindu temples. It is not intended to speak to issues of social justice, or economic questions. It is not intended to imply that all temples are the same, or that all temples are perfect institutions. Other studies exist which treat those topics. This short study can offer only a cursory suggestion of the intricasies of the symbol system, the modes of measuring units and proportions, and the reflection of the whole in some of the parts.

Hindu philosophy views the cosmos to be holonomic and self-similar in nature. The procedures and methods used in the construction of Hindu temples bear a striking resemblance to the procedures of fractal geometry, including discretization, fractalization and extensive use of recursive procedures, with self-similar iteration. The instructions given in ancient Vastu shastras (texts on architecture) work like general programmes to generate various types of temples. The presentation draws attention to the similarities between the procedures and resulting forms in computer graphics and Hindu temple architecture, explain the relationship that exists between the form of the temple and the concepts of Hindu philosophy. It is proposed that Hindu temples may be viewed as examples of 3-dimensional fractal architecture and that the fractal principles used in them along with the parametric and algorithm based-form generation processes, have special significance to the emerging new discipline of Fractal Architecture world-wide.

The second part of the paper shows the applications of the fractal procedures as seen in contemporary architecture as a new methodology of creating architecture which follows a parametric, procedure based form-generation approach, rather than the intuitive approach. The fractal approach leads to an architectural output that is organic and holistic, with an integrated physiognomy similar to that found in natural structures. Fractal principles are drawing great attention in the architectural community, and a large body of work is emerging both as conceptual and also built architectural forms. The presentation illustrates with examples of contemporary works of fractal architecture – both conceptual and built architecture – ranging from individual structures to community networks using parametric modeling; and how thousands of temples in India and Asia built centuries ago provide excellent examples of fractal architecture created through parametric form-generating algorithms.

Presented at the Second International Academic Conference on Modern Oriental Art,
Moscow, 17–20 October, 2017

Author and historian Yuval Harari has foreseen a future where humans emerge as "self-made gods of planet Earth." Yet what may displace Homo Deus as the main mover in evolution? A prime candidate is a hybrid lifeform of greater scope. A new genus of superorganisms – Deus Narrans – will have an opportunity to engage actual and virtual beings across species lines in quests to co-evolve shared values, rather than advance a single genetic and memetic lineage. The art, technology and science endeavors arising from such new transspecies connectives may surpass in influence those of species-bound rivals. Exponential technologies will propel this transition. For eons, material scarcities prompted zero-sum rivalries among and between hominids and other species to reproduce at the expense of one another. As plenitude and longevity grow, new forms of non-zero sum interchange will arise among sentient beings. Evolution in a post-scarcity era will differ from earlier epochs by turning to the spread of lumenes -- replicable qualities of spirit (patterns of emotional response)-across species lines. New communication technologies and pattern languages can speed this shift. Technologies already are emerging for sentient beings to converse and share emotions among distantly-related animal and plant lifeforms. These tools will become central as evolution grows branchier. Genetic engineering and artificial intelligence soon will make Homo Sapiens the ancestor of myriad new cultures and species, many far surpassing our present capabilities. As a common ground for connecting sentient life forms, Deus Narrans can meet the need for spreading empathic resonances, understandings and collaboration among beings across species lines. The heart of such interactions may be a fractal system for co-creation in the realms of art, science, and technology. This paper maps how "social tetrahedrons" and “narrative fractals” can serve as interfaces through which sentient beings of all kinds can share experiences and create value at all scales in multiple realms. In the coming year, open source apps will begin testing such interfaces to bridge current cultural barriers in peer learning and online collaboration. If transcultural pilots succeed, they may set the stage for millions of humans – as well as individuals from new lifeforms to come – to explore, thrive, and co-evolve in relationships made possible by Deus Narrans.

El método comparativo con el que se envaneció la antropología desde sus inicios (y por el que la disciplina fuera cuestionada por todos los relativismos, perspectivismos y decolonialismos que han habido) nunca existió en plenitud hasta bien entrado el siglo que corre. Las nuevas y las viejas ciencias cognitivas, la psicología y las matemáticas saben desde hace tiempo (o deberían saberlo) que la similitud, la diferencia y la analogía nunca han sido operaciones transparentes ni formalmente bien fundadas  hasta prácticamente ahora.

Desclasificada la información de la Guerra Fría, muchos de los logros de las corrientes comparativistas de mediados del siglo XX han quedado borradas del mapa. Los autores comparativistas más reputados (George Peter Murdock es el caso más penoso) han sido -como hoy se dice- "cancelados" sin miramientos  en la investigación contemporánea. Incluso los que pasan por ser los mejores avances de los métodos geométricos de la representación de proximidades y distancias (identificados sin mucha razón con los análisis de Pierre Bourdieu) revelan hoy su estrechez al no poder expresar las matemáticas complejas de la no linealidad y al no distinguir cualitativamente entre un valor de magnitud un poco mayor y otro abismalmente más grande. Las tipificaciones cuantitativas rozan el absurdo al describir los valores extremos como "mayores a X" o "menores que Y" sin especificar el orden de las magnitudes implicadas.

Las últimas revisiones practicadas sobre el texto introdujeron como eje principal las más recientes elaboraciones de la antropología y la arqueología virtual en torno de la geometría morfométrica, capitalizando las innovaciones abiertas por Franz Boas (1905) y devolviendo la iniciativa a nuestras ciencias después de un tiempo demasiado largo en que proliferó el uso acrítico de estadísticas paramétricas y técnicas galtonianas de regresión preñadas de racismo.

Este libro hipertextual explora los mitos urbanos más recónditos y difundidos sobre la comparación, traza el mapa de la casi totalidad de la literatura referida a la idea y ofrece nuevas formas de afrontar ya sea (a) una posible recuperación de los saberes relevantes interpelando los errores ya perpetrados o todavía latentes, o (b) nuevas maneras de llevar a la práctica una disciplina con la que nos hemos malquistado muchas veces (la antropología, por cierto ) pero que sigue mereciendo su lugar en el mundo, tanto o mucho más que otros saberes que el mismo día de hoy siguen ocupando el podio.

Durante un periodo più o meno lungo di relativa stabilità, il sistema riesce a neutralizzare le perturbazioni, ma ad un certo punto elementi pregressi provocano una crisi di instabilità durante la quale i vari elementi del sistema sono sottoposti a tensione, come un gas surriscaldato in cui aumenti progressivamente il movimento delle molecole. La rottura, o biforcazione catastrofica, è preceduta da uno stato caotico in cui ogni minima fluttuazione può essere estremamente amplificata da fenomeni di feedback positivo. Il futuro del sistema diventa imprevedibile se non si conosce la storia delle condizioni al contorno che hanno provocato lo stato attuale (René Thom, determinista; gli indeterministi sostengono invece che il sistema diventa imprevedibile e basta). In tale stato, una fluttuazione più ampia o una sincronia di condizioni catapultano il sistema ad uno stadio superiore il quale procede in un nuovo stato stabile.

Un sistema come quello capitalistico può rimanere stabile, cioè in equilibrio omeostatico, mediante l'autoregolazione dei propri flussi di energia (retroazione negativa, come nel termostato: keynesismo, patto sociale) per un certo periodo, fino al momento in cui i cicli stabilizzanti non vanno in crisi; la retroazione, da negativa diventa positiva (ad esempio sovrapproduzione e speculazione), le perturbazioni si accumulano, ed il sistema esplode in una biforcazione catastrofica verso un nuovo livello di stabilità. L'importante è ciò che succede nel periodo di fluttuazione caotica: in esso si osserva un fenomeno detto di nucleazione, vale a dire che una regione del sistema improvvisamente si auto-organizza in un nuovo ordine fino a raggiungere, via catastrofe, il nuovo assetto, il quale viene di nuovo stabilizzato da una serie di cicli di retroazione.

Desentrañar el origen exacto del perspectivismo, sintetizar sus lineamientos y evaluar su aporte es un trabajo enredado por­que (como habrá de verse) los au­to­res se citan re­cí­pro­ca­mente, copian y pe­gan, se realimentan, descontextualizan y filtran todo tex­to que to­can, en­mascaran sus vo­ces propias tras de un canon de dis­cur­­­si­vi­dad im­per­sonal, reparten pre­mios y castigos discor­dantes, glorifican o domestican fuen­tes de inspiración que difie­ren cada vez que histo­ri­zan sus propias trayec­to­rias, cultivan las más hondas contradic­cio­nes, adoptan ni­ve­les de abs­tracción tan altos que todo lo que miran deviene parecido, atri­bu­yen etno­cen­tris­mo, modernismo o derechismo a quienes piensan distinto, invisibilizan todo lo que guarde relación con pro­cesos de cam­bio, re­su­­ci­tan autores y con­­ceptos en desuso que se han demostrado pro­ble­máticos (sha­ma­­nismo, a­ni­mis­­mo, parti­ci­pa­ción), vuel­ven a llamar o aceptan que se llame “primitivos”, “fósiles”, “bárbaros” o “sal­vajes” a los pue­­blos ori­gi­­na­rios, desa­tien­den todo as­pec­to de la vi­da y la so­­ciedad que no implique el men­­tís de dicotomías más presuntas que reales, agru­pan prác­­ti­cas di­ver­sas en ca­te­gorías uni­­for­­­mes, aguijonean a sus discípulos para que adopten repertorios concep­tua­­les rebuscados que no están aso­ciados a ninguna metodología, a­tri­buyen a la cien­cia, a occi­den­­te o a quien se ponga a tiro ideo­logías que na­die sus­ten­tó o que no han sido exac­ta­mente co­mo se las des­­­cribe, des­co­nocen o des­precian cam­­­pos en­teros del tra­­­­bajo cien­­­tífi­co en general y de la antropología en particular, redu­cen la con­ciencia, la cogni­ción y el pen­sa­miento a la invención mito­ló­gica, importan conceptos de la matemática cruda que no sirven para lo que se requiere, tri­via­li­zan, mi­ni­­mizan o sobre­va­loran los mé­ritos que encuentran en los po­cos an­tropólogos extra­par­ti­da­rios de cu­ya ima­ginación y de cuyo respaldo de­penden (Pie­­­­rre Clas­tres,  Roy Wag­ner, Mar­shall Sahlins, An­tho­ny See­­ger, Ma­­ri­lyn Stra­thern y por su­puesto Clau­de Lévi-Strauss) y les atri­bu­yen una y otra vez ideas que no es­tán ahí cuan­do se lo co­rrobora o que mu­tan de sen­tido o cam­bian de acen­to cuan­do se las con­tem­pla en su contexto real.

Lejos estamos de una teoría de excelencia. Atri­bu­yo al perspectivismo, como sus logros culmi­nan­tes, la más fea definición conocida del pensa­miento indígena, la concepción más bizarra e ingenua de la idea de objeto fractal, la visión de con­junto más insustancial del estado de la teoría y el método en la disciplina y la imple­men­tación más pobre, estúpida y torcida jamás llevada a cabo del con­cepto riemanniano-deleuziano de multi­pli­cidad.

En este libro se examinan críticamente las etapas de la antropología perspectivista Amazónica, desde el animismo de Philippe Descola hasta la antropología pos-estructuralista de Eduardo Viveiros de Castro, pasando por la Teoría del Actor-Red de Bruno Latour, pasando por las ideas de Pierre Clastres, Marilyn Strathern, Bruno Lator y el recientemente fallecido Roy Wagner.

The emergence of chaos and complexity sciences had an influence on philosophy, art and architecture. Scientists and mathematicians found that fractal geometry provides some explanation for nature complexities. This paradigm resulted in a shift in thought which appeared in architecture. Architects have been interested to connect their work to the universe as Frank Lloyd Wright and Peter Eisenman, and tended to design architecture that is based on fractals. Architects created attractive cellular patterns, growing grains like in natural creations and subdividing elements to smaller units. Fractal geometry with its characteristics of self-similarity, scaling and never-ending had a hand in architecture as a formative idea and form generator. Architects, when designing using fractal geometry, tend to use it aesthetically, creating decorative complex patterns which can be perceived by the public. This resulted in use of fractal geometry to design attractive facades. The fractal involvement in the skin design of a building is more apparent than in the architectural morphology of masses and spaces. Patterns generated using fractal geometry are mostly used in skin design which creates the risk that fractal geometry would fall into superficiality and to be applied in a direct and shallow manner. This paper explores the following question; is fractal geometry confined by architects in designing skin and facades of building rather than its original vision of achieving complexity? That is achieved by discussing existing international architectural precedents in which designers used fractal geometry in skin design, regardless of the building type. Through analysis, the paper aims to show that the use of fractal geometry in skin design may actually have a relation with functions and spaces, environmental solutions and other design aspects and considerations. Conference theme: Aesthetics of form

The 1st book of Ra-Ah-Si-Rus, This was originally published as a draft copy in 2015 ( * total solar eclipse at the Spring equinox ) ... and then as its 1st photographic edition in 2016. Since then, 60+ signed copies have been printed and posted around the world. The most up to date version can be downloaded @ www.Infinity-codes.net. All work is done by donation, as I have explained in the book, the world Maths situation, shows that we can't seem to Add up very well as a species, Peace