Building pH Sensors into Paper-based Small-molecular Logic Sys-tems for Very Simple Detection of Edges of Objects

Genetically-engineered bacteria and reactive DNA networks detect edges of objects, as done in our retinas and as also found within computer vision. We now demonstrate that simple molecular logic systems (a combination of a pH sensor, a photo acid generator and a pH buffer spread on paper) without any organization can achieve this relatively complex computational goal with good-fidelity. This causes a jump in the complexity achievable by molecular logic-based computation and extends its applicability. The molecular species involved in light dose-driven 'off-on-off' fluorescence is diverted in the ‘on’ state by proton diffusion from irradiated to unirradiated regions where it escapes a strong quencher, thus visualizing the edge of a mask.

Validation of non‑stationary precipitation series for site‑specific impact assessment: comparison of two statistical downscaling techniques

Statistical downscaling (SD) methods have become a popular, low-cost and accessible means of bridging the gap between the coarse spatial resolution at which climate models output climate scenarios and the finer spatial scale at which impact modellers require these scenarios, with various different SD techniques used for a wide range of applications across the world. This paper compares the Generator for Point Climate Change (GPCC) model and the Statistical DownScaling Model (SDSM)—two contrasting SD methods—in terms of their ability to generate precipitation series under non-stationary conditions across ten contrasting global climates. The mean, maximum and a selection of distribution statistics as well as the cumulative frequencies of dry and wet spells for four different temporal resolutions were compared between the models and the observed series for a validation period. Results indicate that both methods can generate daily precipitation series that generally closely mirror observed series for a wide range of non-stationary climates. However, GPCC tends to overestimate higher precipitation amounts, whilst SDSM tends to underestimate these. This infers that GPCC is more likely to overestimate the effects of precipitation on a given impact sector, whilst SDSM is likely to underestimate the effects. GPCC performs better than SDSM in reproducing wet and dry day frequency, which is a key advantage for many impact sectors. Overall, the mixed performance of the two methods illustrates the importance of users performing a thorough validation in order to determine the influence of simulated precipitation on their chosen impact sector.

Analysis of electric vehicle charging using the traditional generation expansion planning analysis tool WASP-IV

Electric vehicles (EV) are proposed as a measure to reduce greenhouse gas emissions in transport and support increased wind power penetration across modern power systems. Optimal benefits can only be achieved, if EVs are deployed effectively, so that the exhaust emissions are not substituted by additional emissions in the electricity sector, which can be implemented using Smart Grid controls. This research presents the results of an EV roll-out in the all island grid (AIG) in Ireland using the long term generation expansion planning model called the Wien Automatic System Planning IV (WASP-IV) tool to measure carbon dioxide emissions and changes in total energy. The model incorporates all generators and operational requirements while meeting environmental emissions, fuel availability and generator operational and maintenance constraints to optimize economic dispatch and unit commitment power dispatch. In the study three distinct scenarios are investigated base case, peak and off-peak charging to simulate the impacts of EV’s in the AIG up to 2025.

Electric vehicles and opportunities to displace tailgate emissions using Smart Charging controls

Under the European Union Renewable Energy Directive each Member State is mandated to ensure that 10% of transport energy (excluding aviation and marine transport) comes from renewable sources by 2020. The Irish Government intends to achieve this target with a number of policies including ensuring that 10% of all vehicles in the transport fleet are powered by electricity by 2020. This paper investigates the impact of the 10% electric vehicle target in Ireland in 2020 using a dynamic programming based long term generation expansion planning model. The model developed optimizes power dispatch using hourly electricity demand curves up to 2020, while incorporating generator characteristics and certain operational requirements such as energy not served and loss of load probability while satisfying constraints on environmental emissions, fuel availability and generator operational and maintenance costs. Two distinct scenarios are analysed based on a peak and off-peak charging regimes in order to simulate the effects of the electric vehicles charging in 2020. The importance and influence of the charging regimes on the amount of energy used and tailgate emissions displaced is then determined.

Efficiency assessment of electricity power generation on Ireland’s Single Electricity Market by Data Envelopment Analysis

The efficiency of generation plants is an important measure for evaluating the operating performance. The objective of this paper is to evaluate electricity power generation by conducting an All-Island-Generator-Efficiency-Study (AIGES) for the Republic of Ireland and Northern Ireland by utilising a Data Envelopment Analysis (DEA) approach. An operational performance efficiency index is defined and pursued for the year 2008. The economic activities of electricity generation units/plants examined in this paper are characterized by numerous input and output indicators. Constant returns to scale (CRS) and variable returns to scale (VRS) type DEA models are employed in the analysis. Also a slacks based analysis indicates the level of inefficiency for each variable examined. The findings from this study provide a general ranking and evaluation but also facilitate various interesting efficiency comparisons between generators by fuel type.

An approach to determine the local boundary of small disturbance voltage stability region in a cut-set power space:基于微扰的割集电压稳定域局部边界求解方法

A new approach to determine the local boundary of voltage stability region in a cut-set power space (CVSR) is presented. Power flow tracing is first used to determine the generator-load pair most sensitive to each branch in the interface. The generator-load pairs are then used to realize accurate small disturbances by controlling the branch power flow in increasing and decreasing directions to obtain new equilibrium points around the initial equilibrium point. And, continuous power flow is used starting from such new points to get the corresponding critical points around the initial critical point on the CVSR boundary. Then a hyperplane cross the initial critical point can be calculated by solving a set of linear algebraic equations. Finally, the presented method is validated by some systems, including New England 39-bus system, IEEE 118-bus system, and EPRI-1000 bus system. It can be revealed that the method is computationally more efficient and has less approximation error. It provides a useful approach for power system online voltage stability monitoring and assessment. This work is supported by National Natural Science Foundation of China (No. 50707019), Special Fund of the National Basic Research Program of China (No. 2009CB219701), Foundation for the Author of National Excellent Doctoral Dissertation of PR China (No. 200439), Tianjin Municipal Science and Technology Development Program (No. 09JCZDJC25000), National Major Project of Scientific and Technical Supporting Programs of China During the 11th Five-year Plan Period (No. 2006BAJ03A06). ©2009 State Grid Electric Power Research Institute Press.

The application of a novel fluidised photo reactor under UV-Visible and natural solar irradiation in the photocatalytic generation of hydrogen

With advancements in the development of visible light responsive catalysts for H2 production frequently being reported, photocatalytic water splitting has become an attractive method as a potential ‘solar fuel generator’. The development of novel photo reactors which can enhance the potential of such catalyst, however, is rarely reported. This is particularly important as many reactor configurations are mass transport limited, which in term limits the efficiency of more effective photocatalysts in larger scale applications. This paper describes the performance of a novel fluidised photo reactor for the production of H2 over two catalysts under UV-Visible light and natural solar illumination. Catalysts Pt-C3N4 and NaTaO3.La were dispersed in the reactor and the rate of H2 was determined by GC-TCD analysis of the gas headspace. The unit was an annular reactor constructed from stainless steel 316 and quartz glass with a propeller located in the base to control fluidisation of powder catalysts. Reactor properties such as propeller rotational speed were found to enhance the photo activity of the system through the elimination of mass transport limitations and increasing light penetration. The optimum conditions for H2 evolution were found to be a propeller rotational speed of 1035 rpm and 144 W of UV-Visible irradiation, which produced a rate of 89 µmol h-1 g-1 over Pt-C3N4. Solar irradiation was provided by the George Ellery Hale Solar Telescope, located at the California Institute of Technology.

Stochastic analysis of seepage under water-retaining structures

This paper investigated the problem of confined flow under dams and water retaining structuresusing stochastic modelling. The approach advocated in the study combined a finite elementsmethod based on the equation governing the dynamics of incompressible fluid flow through aporous medium with a random field generator that generates random hydraulic conductivity basedon lognormal probability distribution. The resulting model was then used to analyse confined flowunder a hydraulic structure. Cases for a structure provided with cutoff wall and when the wall didnot exist were both tested. Various statistical parameters that reflected different degrees ofheterogeneity were examined and the changes in the mean seepage flow, the mean uplift forceand the mean exit gradient observed under the structure were analysed. Results reveal that underheterogeneous conditions, the reduction made by the sheetpile in the uplift force and exit hydraulicgradient may be underestimated when deterministic solutions are used.

Introducing the CTA concept

The Cherenkov Telescope Array (CTA) is a new observatory for very high-energy (VHE) gamma rays. CTA has ambitions science goals, for which it is necessary to achieve full-sky coverage, to improve the sensitivity by about an order of magnitude, to span about four decades of energy, from a few tens of GeV to above 100 TeV with enhanced angular and energy resolutions over existing VHE gamma-ray observatories. An international collaboration has formed with more than 1000 members from 27 countries in Europe, Asia, Africa and North and South America. In 2010 the CTA Consortium completed a Design Study and started a three-year Preparatory Phase which leads to production readiness of CTA in 2014. In this paper we introduce the science goals and the concept of CTA, and provide an overview of the project. © 2013 Elsevier B.V. All rights reserved.

Implementation of a cogeneration plant for a food processing facility. A case study

The present work presents an investigation regarding the feasibility analysis of a cogeneration plant for a food processing facility with the aim to decrease the cost of energy supply. The monthly electricity and heat consumption profiles are analyzed, in order to understand the consumption profiles, as well as the costs of the current furniture of electricity and gas. Then, a detailed thermodynamic model of the cogeneration cycle is implemented and the investment costs are linked to the thermodynamic variables by means of cost functions. The optimal electricity power of the co-generator is determined with reference to various investment indexes. The analysis highlights that the optimal dimension varies according to the chosen indicator, therefore it is not possible to establish it univocally, but it depends on the financial/economic strategy of the company through the considered investment index.

Ultrastructure and phylogeny of peridinioid dinoflagellates

Os dinoflagelados são um grupo muito diverso de protistas que possuem um conjunto de características pouco comuns. Os peridinióides são dinoflagelados com teca que é formada por seis séries latitudinais de placas, incluindo a série cingular e um anel incompleto de placas intercalares anteriores, embora as últimas estejam ausentes em algumas espécies de Peridiniopsis. São dinoflagelados com simetria bilateral em relação ao plano apical que contem o eixo dorso-ventral. Na série sulcal há apenas uma placa posterior que contacta com o limite ventral de duas grandes placas antapicais. Entre os peridinióides, a presença ou ausência de um poro apical e o número de placas no cíngulo são geralmente consideradas marcas filogenéticas importantes ao nível de género ou família. Actualmente, a definição de Peridinium Ehrenberg, o dinoflagelado mais comum de água doce, inclui organismos com combinações diferentes destas duas características. Trabalhos anteriores sobre a ultrastrutura e afinidade filogenética das espécies tipo de Peridinium, P. cinctum, e Peridiniopsis Lemmermann, P. borgei também sugerem a necessidade de reexaminar as relações taxonómicas dos peridinióides. Esta tese combina o estudo ultrastrutural de uma selecção de espécies com hipóteses filogenéticas baseadas nas sequências de LSU rDNA, para aumentar o nosso conhecimento das diferenças e afinidades dentro dos peridinióides. Tem como objectivo aumentar o nosso conhecimento das características individuais das células que possam levar a reconhecer sinapomorfias que possam ser usadas como marcadores dos peridinióides como um todo e dos seus subgrupos. As espécies escolhidas para exame pormenorizado foram: Peridinium palatinum Lauterborn, de um grupo com duas placas intercalares anteriores, seis placas cingulares e sem poro apical; Peridinium lomnickii Wo!oszy"ska, de um grupo com poro apical, três placas intercalares e seis cingulares; Peridiniopsis berolinensis (Lemmermann) Bourrelly, uma espécie heterotrófica com poro apical, sem placas intercalares e com seis placas cingulares; e Sphaerodinium cracoviense Wo!oszy"ska, um membro de um género de formas com teca com um tipo de tabulação marginalmente peridinióide, com um suposto poro apical e quatro placas intercalares anteriores. Peridinium palatinum difere de Peridinium e Peridiniopsis típicos, quer em características da teca, quer internas. As diferenças estimadas entre as sequências parciais de LSU rDNA de P. palatinum e a espécie próxima P. pseudolaeve, relativamente a P. cinctum são comparativamente grandes e, juntamente com a topologia da árvore filogenética, apoiam a separação de P. palatinum e formas próximas ao nível de género. Palatinus nov. gen. foi, então, descrito com as novas combinações Palatinus apiculatus nov. comb. (espécie tipo; sin. Peridinium palatinum), P. apiculatus var. laevis nov. comb. e P. pseudolaevis nov. comb.. As características distintivas de Palatinus incluem uma superfície das placas lisa ou um tanto granulosa, mas não areolada, um grande pirenóide central penetrado por canais citoplasmáticos e de onde radiam lobos plastidiais, e a presença de uma fiada microtubular homóloga à de um pedúnculo. As células de Palatinus saem da teca pela zona antapicalpos- cingular. Peridinium lomnickii apresenta tabulação semelhante às formas marinhas, produtoras de quistos calcários, do género Scrippsiella A.R. Loeblich. Para comparação, adicionámos novas observações ultrastruturais de S. trochoidea. Peridinium lomnickii tem uma combinação de características diferente de Peridinium, Peridiniopsis e Scrippsiella. As hipóteses filogenéticas baseadas em DNA colocam P. lomnickii no mesmo ramo que Pfiesteria Steidinger et Burkholder, Tyrannodinium e outras Pfiesteriaceae, com as quais partilha um "microtubular basket" e uma ligação peculiar entre duas placas do sulco. As características distintivas do novo género proposto Chimonodinium gen. ined. incluem, além da tabulação, a ausência de pirenóides, a presença de um "microtubular basket" com quatro ou cinco fiadas sobrepostas de microtúbulos associados a um pequeno pedúnculo, um sistema pusular com tubos pusulares bem definidos ligados aos canais flagelares, e a produção de quistos não calcários. Peridiniopsis berolinensis partilha várias características significativas com Pfiesteria e afins, como um "microtubular basket" com a capacidade de suportar um tubo de alimentação, quimiossensibilidade para encontrar presas apropriadas, o modo de natação junto às presas e a organização geral da célula. Hipóteses filogenéticas com base em LSU rDNA confirmam a afinidade entre P. berolinensis e Pfiesteria bem como a relação mais remota com a espécie tipo de Peridiniopsis, P. borgei. Estas razões justificam a proposta de Tyrannodinium gen. nov., uma nova Pfiesteriaceae que difere de outros membros do grupo por viver em água doce e nos pormenores da tabulação. Sphaerodinium cracoviense revelou a tabulação típica do género Sphaerodinium, que apresenta um número de placas intercalares superiores e pos-cingulares maior que o que é típico em peridinióides: 4 e 6, respectivamente. Observações em SEM mostraram uma estrutura apical diferente da dos peridinióides, e um sulco apical numa das placas fazendo lembrar a área apical de alguns woloszynskióides. Os pormenores do aparelho flagelar e do sistema pusular ligam o Sphaerodinium aos woloszynskióides em geral e ao género Baldinia em particular, mas não aos peridinióides. O volumoso estigma de S. cracoviense revelou ser extraplastidial e de um modelo único, composto por elementos que se encontram em woloszynskióides, mas nunca encontrados anteriormente juntos. A análise filogenética baseada nas sequências parciais de LSU rDNA também sugerem uma maior proximidade de S. cracoviense com os woloszynskióides do que com os peridinióides. Futuras análises pormenorizadas de dinoflagelados peridinióides, em especial entre os do numeroso grupo de espécies com poro apical, serão necessárias para clarificar as suas relações taxonómicas; e a produção de descrições melhoradas das características finas particulares das células serão um requisito para perceber a evolução dos caracteres dos peridinióides por forma a podermos identificar marcadores filogenéticos.

Dimensioning of multilayer optical networks

Este trabalho apresenta um estudo sobre o dimensionamento de redes ópticas, com vistas a obter um modelo de dimensionamento para redes de transporte sobreviventes. No estudo utilizou-se uma abordagem estatística em detrimento à determinística. Inicialmente, apresentam-se as principais tecnologias e diferentes arquitecturas utilizadas nas redes ópticas de transporte. Bem como os principais esquemas de sobrevivência e modos de transporte. São identificadas variáveis necessárias e apresenta-se um modelo dimensionamento para redes de transporte, tendo-se dado ênfase às redes com topologia em malha e considerando os modos de transporte opaco, transparente e translúcido. É feita uma análise rigorosa das características das topologias de redes de transporte reais, e desenvolve-se um gerador de topologias de redes de transporte, para testar a validade dos modelos desenvolvidos. Também é implementado um algoritmo genético para a obtenção de uma topologia optimizada para um dado tráfego. São propostas expressões para o cálculo de variáveis não determinísticas, nomeadamente, para o número médio de saltos de um pedido, coeficiente de protecção e coeficiente de restauro. Para as duas últimas, também é analisado o impacto do modelo de tráfego. Verifica-se que os resultados obtidos pelas expressões propostas são similares às obtidas por cálculo numérico, e que o modelo de tráfego não influencia significativamente os valores obtidos para os coeficientes. Finalmente, é demonstrado que o modelo proposto é útil para o dimensionamento e cálculo dos custos de capital de redes com informação incompleta.

Study of multiferroic materials

The present PhD work aims the research and development of materials that exhibit multiferroic properties, in particular having a significant interaction between ferromagnetism and ferroelectricity; either directly within an intrinsic single phase or by combining extrinsic materials, achieving the coupling of properties through mechanic phenomena of the respective magnetostriction and piezoelectricity. These hybrid properties will allow the cross modification of magnetic and electric polarization states by the application of cross external magnetic and/or electric fields, giving way to a vast area for scientific investigation and potential technological applications in a new generation of electronic devices, such as computer memories, signal processing, transducers, sensors, etc. Initial experimental work consisted in chemical synthesis of nano powders oxides by urea pyrolysis method: A series of ceramic bulk composites with potential multiferroic properties comprised: of LuMnO3 with La0.7Sr0.3MnO3 and BaTiO3 with La0.7Ba0.3MnO3; and a series based on the intrinsic multiferroic LuMn1-zO3 phase modified with of Manganese vacancies. The acquisition of a new magnetron RF sputtering deposition system, in the Physics Department of Aveiro University, contributed to the proposal of an analogous experimental study in multiferroic thin films and multilayer samples. Besides the operational debut of this equipment several technical upgrades were completed like: the design and construction of the heater electrical contacts; specific shutters and supports for the magnetrons and for the substrate holder and; the addition of mass flow controllers, which allowed the introduction of N2 or O2 active atmosphere in the chamber; and the addition of a second RF generator, enabling co-deposition of different targets. Base study of the deposition conditions and resulting thin films characteristics in different substrates was made from an extensive list of targets. Particular attention was given to thin film deposition of magnetic phases La1-xSrxMnO3, La1-xBaxMnO3 and Ni2+x-yMn1-xGa1+y alloy, from the respective targets: La0.7Sr0.3MnO3, La0.7Ba0.3MnO3; and NiGa with NiMn. Main structural characterization of samples was performed by conventional and high resolution X-Ray Diffraction (XRD); chemical composition was determined by Electron Dispersion Spectroscopy (EDS); magnetization measurements recur to a Vibrating Sample Magnetometer (VSM) prototype; and surface probing (SPM) using Magnetic-Force (MFM) and Piezo-Response (PFM) Microscopy. Results clearly show that the composite bulk samples (LuM+LSM and BTO+LBM) feat the intended quality objectives in terms of phase composition and purity, having spurious contents below 0.5 %. SEM images confirm compact grain packaging and size distribution around the 50 nm scale. Electric conductivity, magnetization intensity and magneto impedance spreading response are coherent with the relative amount of magnetic phase in the sample. The existence of coupling between the functional phases is confirmed by the Magnetoelectric effect measurements of the sample “78%LuM+22%LSM” reaching 300% of electric response for 1 T at 100 kHz; while in the “78%BTO+22%LBM” sample the structural transitions of the magnetic phase at ~350 K result in a inversion of ME coefficient the behavior. A functional Magneto-Resistance measurement system was assembled from the concept stage until the, development and operational status; it enabled to test samples from 77 to 350 K, under an applied magnetic field up to 1 Tesla with 360º horizontal rotation; this system was also designed to measure Hall effect and has the potential to be further upgraded. Under collaboration protocols established with national and international institutions, complementary courses and sample characterization studies were performed using Magneto-Resistance (MR), Magneto-Impedance (MZ) and Magneto-Electric (ME) measurements; Raman and X-ray Photoelectron Spectroscopy (XPS); SQUID and VSM magnetization; Scanning Electron Microscopy (SEM) and Rutherford Back Scattering (RBS); Scan Probe Microscopy (SPM) with Band Excitation Probe Spectroscopy (BEPS); Neutron Powder Diffraction (NPD) and Perturbed Angular Correlations (PAC). Additional collaboration in research projects outside the scope of multiferroic materials provided further experience in sample preparation and characterization techniques, namely VSM and XPS measurements were performed in cubane molecular complex compounds and enable to identify the oxidation state of the integrating cluster of Ru ions; also, XRD and EDS/SEM analysis of the acquired targets and substrates implied the devolution of some items not in conformity with the specifications. Direct cooperation with parallel research projects regarding multiferroic materials, enable the assess to supplementary samples, namely a preliminary series of nanopowder Y1-x-yCaxØyMn1O3 and of Eu0.8Y0.2MnO3, a series of micropowder composites of LuMnO3 with La0.625Sr0.375MnO3 and of BaTiO3 with hexagonal ferrites; mono and polycrystalline samples of Pr1-xCaxMnO3, La1-xSrxMnO3 and La1-xCaxMnO3.

A new combined joules supercritical rankine cycle exergetic analysis and optimization

The application of a supercritical Rankine cycle in combined cycles does not happen in today’s thermoelectric power stations. Nevertheless, the most recent development in gas turbines, that allows a high efficiency and high exhaust gases temperatures, and the improvement of high pressure and temperature alloys, makes this cycle possible. This study’s intent is to prove the viability of this combined cycle, since it can break the 60% efficiency barrier, which is the plafond in actual power stations. To attain this target, several configurations for this cycle have been simulated, optimized and analyzed [1]. The simulations were done with the computational program IPSEpro [2] and the optimizations were effectuated with software developed for the effect, using the DFP method [3]. In parallel with the optimization that claims the cycle’s efficiency maximization, an exergetic analysis was also made [4] to all the cycle components. In opposite to what happens in subcritical combined cycles, it was demonstrated that in supercritical combined cycles the higher efficiency takes place with a single steam pressure in the heat recovery steam generator (HRSG).

Entwicklung von Verfahren zur visuellen Beurteilung von Stabilitätseigenschaften nichtlinearer, zeitdiskreter Systeme

In dieser Arbeit werden Verfahren zur visuellen Beurteilung von Stabilitätseigenschaften nichtlinearer, zeitdiskreter Systeme und mögliche Anwendungen vorgestellt. Ausgehend von den erforderlichen Grundbegriffen der Chaostheorie werden verschiedene Maße zur Detektion, Beschreibung und Visualisierung chaotischen Systemverhaltens motiviert, mathematisch definiert, physikalisch interpretiert und gedeutet: der Lyapunov Exponent, die Entropie, das Fourierspektrum und die Korrelation. Als erste Anwendung basierend auf diesen Gütemaßen wird das Verhalten von linearen und nichtlinearen rekursiven Systemen visualisiert und verglichen. Es zeigt sich, dass bei rekursiven linearen Systemen der Übergang von einem stabilen in einen instabilen oder chaotischen Zustand kontinuierlich erfolgt, während dieser Übergang bei nicht linearen Systemen häufig abrupt auftritt. Unter Verwendung der vorgestellten Visualisierung lässt sich sehr genau nachvollziehen, welche Parameter und insbesondere welche Parameterübergänge dabei kritisch sind. Diese Kenntnis ist sehr wichtig für eine störfreie Systemparametrierung und eine erforderliche Arbeitspunktsuche. In einer zweiten Anwendung wird chaotisches Systemverhalten als Generator optimal orthogonaler Signalfunktionen eingesetzt. Dazu wird die Rekursionsfolge in einem chaotischen Arbeitspunkt eines nichtlinearen rekursiven Systems als Musterfunktion eines statistischen Zufallsprozesses interpretiert: Je chaotischer das Systemverhalten und je kleiner die Varianz des Korrelationsmaßes desto besser können orthogonale Signalfolgen modelliert werden. Solche Signalfolgen sind von großer Bedeutung, wenn digitale Nachrichten über einen gestörten Kanal mit minimalem Daten- und Energieaufwand übertragen werden sollen. Als abschließendes Beispiel wird die fraktale Bildcodierung vorgestellt. Sie beruht nicht wie die klassischen Verfahren der Bildcodierung (Prädiktion, Transformation) auf statistischen Eigenschaften des Bildsignals sondern ausschließlich auf Selbstähnlichkeit. Die Bildpunkte eines Bildblockes werden nicht durch deren Grauwerte sondern durch ein Fraktal beschrieben, wobei dieses Fraktal durch eine kontraktive, affine Abbildung der Grauwertinformation dargestellt wird. Dieses Fraktal, d.h. diese Abbildungsvorschrift oder Gesetzmäßigkeit beschreibt die vollständige Information des Bildes. Durch die Anwendung dieser fraktalen Darstellung wird das codierte Bild aus beliebigen Bildern gleicher Größe generiert.