L-system Research Articles

ERoots: A three-dimensional dynamic growth model of rice roots coupled with soil

Root architecture systems (RAS) reflect the spatial structure of roots in soil. To clarify the structure and distribution of rice roots and investigate the coupling between roots and soil, wetland rice was selected as the experimental object, and a three-dimensional (3D) growth model of rice root environment-roots (ERoots) based on the parameter Lindenmayer system (L-system) was proposed. ERoots combines a root morphological structure model with a growth model and defines L-system grammar iteration rules with the unit time and unit step length as parameters. At the same time, the basic growth parameters of rice roots were obtained via destructive detection, and 3D growth visualisation of roots was realised via MATLAB. In the soil coupling process, a soil nutrient simulation map was constructed based on the spatial soil characteristics per unit volume, and an adjustment strategy for roots reaching the growth boundary was designed. The flexibility of the model coupled with soil was reflected in the tropisms of root growth, growth rate and root branching strategy. Finally, combined with soil spatial characteristic simulation, geometric growth boundary and 3D root growth model, the ability of 3D growth visualisation of rice roots was verified under three soil conditions: (1) unconfined root growth, (2) confined spatial root growth, and (3) root growth with tropisms. The results indicated that the ERoots root model basically realised coupling with soil and achieved a satisfactory simulation effect in regard to the rice morphological structure. This study provides a reference for 3D growth modelling and visualisation of other crop roots.

ETHNOMODELLING: FRACTAL GEOMETRY ON THE DOOR ORNAMENT OF THE SUMENEP PALACE USING THE LINDENMAYER SYSTEM

The Sumenep Palace area is one of the cultural heritage relics of the Duke of Sumenep, which is still preserved today. This research aims to reveal the fractal model of door ornament in the Koneng Office of Sumenep Palace. A qualitative method with an ethnography type is used. Data were collected through initial observation, literature study, interviews, and documentation. Analysis of the fractal form is done with the Lindenmayer system method and constructed with the help of the L-Studio application. The results of the study revealed the existence of fractal structures on the door ornament of the Sumenep palace office. The length, angle, and ratio of each part of the ornament influence the fractal shape. The findings of this study can be utilized in learning mathematics in lectures, such as fractal geometry and computational geometry.

An investigation of the effect of randomness in trunk size and location on the attenuation of sound through forests generated by Lindenmayer systems

This presentation provides an overview of what is known about the influence of randomness in trunk size and location on the attenuation of sound through forests. It also provides an explanation of the Lindenmayer system (L-system) approach to modeling plants and trees in addition to the multiset L-system approach to modeling the dynamics of forest ecosystems, investigating its applicability to the problem of optimizing sound attenuation through forests. This project was completed in partial fulfillment of the requirements for the Diploma in Acoustics and Noise Control, Institute of Acoustics, Milton Keynes, UK, under the mentorship of Dr. Keith Attenborough.

Training of a deep learning based digital subtraction angiography method using synthetic data.

Digital subtraction angiography (DSA) is a fluoroscopy method primarily used for the diagnosis of cardiovascular diseases (CVDs). Deep learning-based DSA (DDSA) is developed to extract DSA-like images directly from fluoroscopic images, which helps in saving dose while improving image quality. It can also be applied where C-arm or patient motion is present and conventional DSA cannot be applied. However, due to the lack of clinical training data and unavoidable artifacts in DSA targets, current DDSA models still cannot satisfactorily display specific structures, nor can they predict noise-freeimages. In this study, we propose a strategy for producing abundant synthetic DSA image pairs in which synthetic DSA targets are free of typical artifacts and noise commonly found in conventional DSA targets for DDSA modeltraining. More than 7,000 forward-projected computed tomography (CT) images and more than 25,000 synthetic vascular projection images were employed to create contrast-enhanced fluoroscopic images and corresponding DSA images, which were utilized as DSA image pairs for training of the DDSA networks. The CTprojection images and vascular projection images were generated from eight whole-body CT scans and 1,584 3D vascular skeletons, respectively. All vessel skeletons were generated with stochastic Lindenmayer systems. We trained DDSA models on this synthetic dataset and compared them to the trainings on a clinical DSA dataset, which contains nearly 4,000 fluoroscopic x-ray images obtained from different models ofC-arms. We evaluated DDSA models on clinical fluoroscopic data of different anatomies, including the leg, abdomen, and heart. The results on leg data showed for different methods that training on synthetic data performed similarly and sometimes outperformed training on clinical data. The results on abdomen and cardiac data demonstrated that models trained on synthetic data were able to extract clearer DSA-like images than conventional DSA and models trained on clinical data. The models trained on synthetic data consistently outperformed their clinical data counterparts, achieving higher scores in the quantitative evaluation of peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) metrics for DDSA images, as well as accuracy, precision, and Dice scores for segmentation of the DDSAimages. We proposed an approach to train DDSA networks with synthetic DSA image pairs and extract DSA-like images from contrast-enhanced x-ray images directly. This is a potential tool to aid indiagnosis.

REWRITING THE ARCHITECTURE OF TRADITIONAL HOUSES OF DYARBAKIR WITH LINDENMAYER SYSTEMS

Doğaya yönelim içeren mimari tasarımlar tasarımcıyı raslantısallıktan uzaklaştırdığı gibi doğaya karşı olan sorumluluğun fark edilmesini sağlamaktadır. Aynı zamanda doğa ile uyumlu tasarımlar, doğaya yönelik kazanımlar elde edilmesini sağlamakta ve yapı sektörünün çevreye verdiği zararı azaltmaktadır. Bu doğrultuda ekoloji ile uyum içerisinde olan Diyarbakır geleneksel evlerinin; yapısal analizleri sonucunda elde edilen verilerin günümüz konutlarına örnek teşkil etmesi açısından temel ilkelerinin referans alınması gerektiği düşünülmektedir. Günümüzde yaşanan teknolojik gelişmeler birçok avantaj sağlamakla beraber doğadan kopuk yapılaşmaların artmasına da sebep olmuştur. Doğa ile uyum göstermeyen yapıların artması günümüzde çevresel anlamda birçok problemin ortaya çıkmasına sebebiyet vermiştir. Bu açıdan çalışma, Diyarbakır geleneksel evlerinin; yapısal analizleri sonucunda elde edilen ilkeler ile günümüz çağdaş konut üretimi için model önerisinde bulunulması gerektiğine odaklanmıştır. Bu çalışmada; araştırma sahası olarak seçilen Diyarbakır Suriçi bölgesinde bulunan 35 adet U plan tipli geleneksel evin planları Lindenmayer sistemler üzerinden yapılan çözümlemelere dayanarak bir model önerisi hazırlamak amaçlanmıştır. Hesaplamalı bilimlerin katkıları ile ortaya çıkan tasarımlardan üretken tasarım yaklaşımı incelenmiş, üretken bir algoritma olan Lindenmayer sistemlerinin mimari tasarımdaki kullanımı ve sürdürülebilirlik ile ilişkisi ele alınmıştır. Doğa-insan etkileşiminin mimarlıktaki yansıma biçimleri olan binalar, bu sistemler özelinde analiz edilmiş, incelenen plan tipolojileri bina yönlenme parametresi esas alınarak yeniden kodlanmıştır. Elde edilen verilerden yola çıkarak, Diyarbakır şehrinin iklimi ve geleneksel mimarisiyle uyumlu, farklı kullanıcılara hitap edebilecek 4 farklı alternatif ideal konut tipolojisi üretilmiştir.

Ethnomathematics: Exploration of Fractal Geometry in Gate Ornaments of the Sumenep Jamik Mosque Using the Lindenmayer System

Jamik Sumenep Mosque, a heritage site of the Sumenep Kingdom, was built to emphasize the acculturation of Chinese, Islamic, and Madurese cultures. This ethnomathematics research aims to reveal and explore the fractal geometry forms in the gateway of Jamik Sumenep Mosque. This study employed qualitative methods with an ethnographic approach. Research data were gathered through observation, field notes, documentation, interviews, and literature studies. Field observations were computationally analyzed using the Lindenmayer system through the L-Studio application to examine fractal shapes. The study found that the length and angle size of the ornamental parts form the basis of fractal geometry in the mosque gateway's ornamentation, thereby confirming the presence of fractal geometry concepts. These findings can be utilized in teaching fractal geometry, applied mathematics, and computational geometry. Further research could explore non-Euclidean geometry methods, such as stochastic L-system methods.

Lattice Based Communication P Systems

Lattice based communication P (LTC-P) systems are a class of extended P systems with lattice membrane structures. This new P-system is recently proposed in our work and LTC-P systems have been shown to be computational completeness. LTC-P systems can efficiently solve some kinds of combination-optimization problems. The purpose of this paper is to investigate the computation power of LTC-P systems through comparison with Chomsky families and Lindenmayer system. The formal framework of LTC-P systems is also provided. Then, we use LTC-P systems to solve SAT and HPP in linear time. Results have shown that LTC-P systems have comparative advantage in the use of membrane numbers.

Latent L-systems: Transformer-based Tree Generator

We show how a Transformer can encode hierarchical tree-like string structures by introducing a new deep learning-based framework for generating 3D biological tree models represented as Lindenmayer system (L-system) strings. L-systems are string-rewriting procedural systems that encode tree topology and geometry. L-systems are efficient, but creating the production rules is one of the most critical problems precluding their usage in practice. We substitute the procedural rules creation with a deep neural model. Instead of writing the rules, we train a deep neural model that produces the output strings. We train our model on 155k tree geometries that are encoded as L-strings, de-parameterized, and converted to a hierarchy of linear sequences corresponding to branches. An end-to-end deep learning model with an attention mechanism then learns the distributions of geometric operations and branches from the input, effectively replacing the L-system rewriting rule generation. The trained deep model generates new L-strings representing 3D tree models in the same way L-systems do by providing the starting string. Our model allows for the generation of a wide variety of new trees, and the deep model agrees with the input by 93.7% in branching angles, 97.2% in branch lengths, and 92.3% in an extracted list of geometric features. We also validate the generated trees using perceptual metrics showing 97% agreement with input geometric models.

Watson-crick (D)0 L systems: a survey

AbstractWatson-Crick L systems are string generating formal models obtained by augmenting Lindenmayer systems with the Watson-Crick morphism inspired by the Watson-Crick complementarity principle. The Watson-Crick morphism is controlled by a trigger—a boolean condition eventually met by the generated word. Despite their simplicity, Watson-Crick (D)0 L systems have interesting mathematical properties, a strong generative power, and they can also characterize some open decision problems. Furthermore, networks of Watson-Crick D0L systems are capable of trading space for time, and thus of characterizing linear time solutions to intractable problems. We provide a survey of results in this field since its origin in 1997 to the present, and we conclude with a series of open research problems and ideas.

Ethnomathematics: The exploration of fractal geometry in Tian Ti Pagoda using the Lindenmayer system

This study explores the concept of fractal geometry found in the Tian Ti Pagoda. Fractal geometry is a branch of mathematics describing the properties and shapes of various fractals. A qualitative method with an ethnographic approach is used in this study. Observation, field notes, interviews, documentation, and literature study obtained research data. The observation results were processed computationally using the Lindenmayer system method via the L-Studio application to view fractal shapes. The results show that the concept of fractal geometry is contained in the ornaments on the Tian Ti Pagoda. The length and angles of each part of the ornament influence the fractal shape of the Tian Ti Pagoda ornament. In addition, the length and angle modifications resulted in several variations of the Tian Ti Pagoda fractal. The findings from this study can be used as an alternative medium for learning mathematics lectures, especially in applied mathematics, dynamical systems, and computational geometry.

Intermediate Encoding Layers for the Generative Design of 2D Soft Robot Actuators: A Comparison of CPPN’s, L-Systems and Random Generation

This paper introduced a comparison method for three explicitly defined intermediate encoding methods in generative design for two-dimensional soft robotic units. This study evaluates a conventional genetic algorithm with full access to removing elements from the design domain using an implicit random encoding layer, a Lindenmayer system encoding mimicking biological growth patterns and a compositional pattern producing network encoding for 2D pattern generation. The objective of the optimisation problem is to match the deformation of a single actuator unit with a desired target shape, specifically uni-axial elongation, under internal pressure. The study results suggest that the Lindenmayer system encoding generates candidate units with fewer function evaluations than the traditional implicitly encoded genetic algorithm. However, the distribution of constraint and internal energy is similar to that of the random encoding, and the Lindenmayer system encoding produces a less diverse population of candidate units. In contrast, despite requiring more function evaluations than the Lindenmayer System encoding, the Compositional Pattern Producing Network encoding produces a similar diversity of candidate units. Overall, the Compositional Pattern Producing Network encoding results in a proportionally higher number of high-performing units than the random or Lindenmayer system encoding, making it a viable alternative to a conventional monolithic approach. The results suggest that the compositional pattern producing network encoding may be a promising approach for designing soft robotic actuators with desirable performance characteristics.

Gas production from shale reservoirs with bifurcating fractures: A modified quadruple-domain model coupling microseismic events

Many fracture branches are generated during hydraulic fracturing to form complex fracture networks and the majority of the gas in the unstimulated region (USR) is left unexploited. Traditional models usually overlook the key effect of bifurcating fracture morphology on gas production from hydraulically stimulated shale formation. Understanding the interaction behavior between the matrix system and the bifurcating fractures is important for exploiting shale reservoirs. In this regard, a modified quadruple-domain model with both the stimulated region (SR) and the USR, is established. The SR contains the bifurcating hydraulic fractures (BHF) which are captured by the Lindenmayer system (L-system) algorithm based on the coupling with microseismic events. Meanwhile, the effects of single layer and multiple layer sorption on gas transport are included in the new dynamic permeability equation. The model is validated against results from the experiment, field data, and numerical simulations. The results demonstrate that the initial axiom, bifurcating distance, deviation angle, and number of iterations have a significant influence on the morphology of the BHF and subsequently control its growth leading to complex network. BHF complexity, natural fracture geometry, and the amount of sorption gas simultaneously determine the flow behavior and cumulative production performance.

Stochastic L-system inference from multiple string sequence inputs

Lindenmayer systems (L-systems) are a grammar system that consists of string rewriting rules. The rules replace every symbol in a string in parallel with a successor to produce the next string, and this procedure iterates. In a stochastic context-free L-system (S0L-system), every symbol may have one or more rewriting rule, each with an associated probability of selection. Properly constructed rewriting rules have been found to be useful for modeling and simulating some natural and human engineered processes where each derived string describes a step in the simulation. Typically, processes are modeled by experts who meticulously construct the rules based on measurements or domain knowledge of the process. This paper presents an automated approach to finding stochastic L-systems, given a set of string sequences as input. The implemented tool is called the Plant Model Inference Tool for S0L-systems or PMIT-S0L. PMIT-S0L is evaluated using 960 procedurally generated S0L-systems in a test suite, which are each used to generate input strings, and PMIT-S0L is then used to infer the system from only the sequences. The evaluation shows that PMIT-S0L infers S0L-systems with up to 9 rewriting rules each in under 12 hours. Additionally, it is found that 3 sequences of strings are sufficient to find the correct original rewriting rules in $$100\%$$ of the cases in the test suite, and 6 sequences of strings reduce the difference in the associated probabilities to approximately $$1\%$$ or less.

Genetic algorithm for the design of a multiband microstrip antenna with self‐avoiding geometry obtained by backtracking

SummaryThe growth of small communication devices has pushed designers to design compact‐size antennas. These antennas must be low cost, lightweight, needed for mechanically robust construction, and ease of installation. In this paper, we use a novel genetic algorithm (GA) to produce an ensemble of compact self‐avoiding (SA) antennas such that the voltage standing wave ratio (VSWR) is less than 2 at the desired frequencies (as a measure of efficiency); an optimization criterion to get a desirable multiband antenna in the ultra high frequency (UHF) band. First, the electromagnetic properties of these antennas are simulated using the method of moments in MATLAB. SA antennas form a particular set of dipoles introduced here by applying a novel backtracking algorithm. We also use a Lindenmayer system that generates the geometries by a Turtle graphics render to reach our goal. Next, we simulate the VSWR for 150,000 SA antennas with lengths from 0.1 to 0.4 m; 10 different frequencies are chosen randomly within the UHF band to obtain our results. All the VSWR 2 are clustered using density‐based spatial clustering of applications with noise algorithm (DBSCAN), so our method provides the frequency ranges where this condition is fulfilled. From this, we obtain the VSWR minimums used for the antenna design. Finally, as an instance, we use our results to select the appropriate size of a multiband antenna and, through genetic algorithms, modify the geometry to satisfy the design requirements.

Procedural Foliage Generation

Abstract: Procedural foliage generation refers to the generation of flora features, through the use of algorithms, with minimal input required from the user. In the process of game development, generating foliage is often an important part of the game development process. Traditional generation methods are often too time-consuming, especially with larger foliage variety. On the other hand, procedural methods that generate foliage automatically often do not have much user control over the output. We explore the usage of Lindenmayer systems in the creation of tree assets. Keywords: Procedural Generation, Computer Graphics, Lindenmayer Systems, Foliage Generation

3D Structural Model and Visualization of Blood Vessels Based on L-System

The insight in structures of the blood vessels is a basis for study of blood flows to help understanding the abnormalities of blood vessels that can cause vascular diseases. Basic concept used for constructing structures of blood vessels in organs is arterial branching, which is usually characterized by fractal similarity in the bifurcation pattern. In this work, the concept of Lindenmayer system (L-system) is modified for three-dimensional (3D) tree-like structures to model structures of blood vessels in organs, and then, applied to construct and visualize structural blood vessels via our software created based on openGL and Lazarus program. The structure of blood vessels is constructed based on the physiological law of arterial branching proposed Murray (Murray’s law) under additional assumptions and constraints such as the spreading of blood vessels to cover all directions, the angle condition and the non-overlapping vessels condition. The concept is applied to simulate structures of blood vessels in 3 study cases, including symmetric arterial branching, non-symmetric arterial branching and structure of blood vessel on different domains. The results of structures of blood vessels generated from all cases are measured based on the number of segments, the total blood volume and the fractal dimension. The results of modeling and simulation in this work are illustrated by comparing with other results appeared literature. Moreover, the constructed structures of the blood vessels based on this 3D L-system could be useful for future research such as blood flow, pressure and other properties involving in structures of blood vessels in different organs of human and animals.
 HIGHLIGHTS
 
 A new 3D L-system is developed based on directional vectors for construction of 3D tree-like structures such as structures of blood vessels
 The model of structures of blood vessels is constructed based on the physiological laws of arterial branching (Murray’s law) with additional assumptions on the spreading of blood vessels, the angle condition, and the non-overlapping of blood vessels
 Algorithm and software are developed based on L-system to simulate and visualize 3D structures of blood vessels
 
 GRAPHICAL ABSTRACT

Development of anatomically based structure for human acinus by Lindenmayer system: accurate model for gas exchange in human lung

Development of anatomically based structure for human acinus by Lindenmayer system: accurate model for gas exchange in human lung

Evolving deep neural networks for Time Series Forecasting

The aim of this paper is to introduce a biologically inspired approach that can automatically generate Deep Neural networks with good prediction capacity, smaller error and large tolerance to noises. In order to do this, three biological paradigms were used: Genetic Algorithm (GA), Lindenmayer System and Neural Networks (DNNs). The final sections of the paper present some experiments aimed at investigating the possibilities of the method in the forecast the price of energy in the Brazilian market. The proposed model considers a multi-step ahead price prediction (12, 24, and 36 weeks ahead). The results for MLP and LSTM networks show a good ability to predict peaks and satisfactory accuracy according to error measures comparing with other methods.

Modeling Plant Stems Using the Deterministic Lindenmayer System

Plant morphology modeling can be done mathematically which includes roots, stems, leaves, to flower. Modeling of plant stems using the Lindenmayer System (L-system) method is a writing returns that are repeated to form a visualization of an object. Deterministic L-system method is carried out by predicting the possible shape of a plant stem using its iterative writing rules based on the original object photo. The purpose of this study is to find a model of the plant stem with Deterministic Lindenmayer System method which will later be divided into two dimensional space three. The research was conducted by identifying objects in the form of pine tree trunks measured by the angle, thickness, and length of the stem. Then a deterministic and parametric model is built with L-system components . The stage is continued by visualizing the model in two dimensions and three dimensions. The result of this research is a visualization of a plant stem model that is close to the original. Addition color, thickness of the stem, as well as the parametric writing is done to get the results resembles the original. The iteration is limited to less than 20 iterations so that the simulation runs optimal.

Techniques for inferring context-free Lindenmayer systems with genetic algorithm

Lindenmayer systems (L-systems) are a formal grammar system, where the most notable feature is a set of rewriting rules that are used to replace every symbol in a string in parallel; by repeating this process, a sequence of strings is produced. Some symbols in the strings may be interpreted as instructions for simulation software. Thus, the sequence can be used to model the steps of a process. Currently, creating an L-system for a specific process is done by hand by experts through much effort. The inductive inference problem attempts to infer an L-system from such a sequence of strings generated by an unknown system; this can be thought of as an intermediate step to inferring from a sequence of images. This paper evaluates and analyzes different genetic algorithm encoding schemes and mathematical properties for the L-system inductive inference problem. A new tool, the Plant Model Inference Tool for Context-Free L-systems (PMIT-D0L) is implemented based on these techniques. PMIT-D0L has been successfully evaluated on 28 known L-systems, with alphabets up to 31 symbols and a total sum of 281 symbols across the rewriting rules. PMIT-D0L can infer even the largest of these L-systems in less than a few seconds.