阅读说明：本技术 一种水生植物根系立体几何构型的构建方法 (Method for constructing three-dimensional geometric configuration of aquatic plant root system ) 是由 黄晓龙 李松阳 李宽意 于 2021-08-24 设计创作，主要内容包括：本发明公开了一种水生植物根系立体几何构型的构建方法,包括如下步骤：1)通过扫描仪获取高分辨率水生植物根系图像；2)对根系图像进行处理,得出根系一级侧根个数、一级侧根长度、二级侧根个数、二级侧根长度、二级侧根直径、顶端不分枝区域长度、末端不分枝区域长度、分支间距、分支数目、主根与根毛夹角和/或初始生长速度的结构数据；3)建立根系的几何构型。本发明实现了水生植物根系构型可视化,可以较为较真实地模拟水生植物根系的生长过程,为研究分析根系周围营养元素对水生植物根系生长发育的可塑性影响等提供了一种简单直观的工具,为水生植物保护、管理和生态修复等提供了科学依据。(The invention discloses a method for constructing a solid geometric configuration of a root system of an aquatic plant, which comprises the following steps: 1) acquiring a high-resolution aquatic plant root system image through a scanner; 2) processing the root system image to obtain structural data of the number of primary lateral roots, the length of the primary lateral roots, the number of secondary lateral roots, the length of the secondary lateral roots, the diameter of the secondary lateral roots, the length of a top non-branching region, the length of a tail end non-branching region, branch spacing, the number of branches, the included angle between a main root and root hairs and/or the initial growth speed of the root system; 3) the geometric configuration of the root system is established. The invention realizes the visualization of the configuration of the aquatic plant root system, can simulate the growth process of the aquatic plant root system more truly, provides a simple and intuitive tool for researching and analyzing the plasticity influence of nutrient elements around the root system on the growth and development of the aquatic plant root system, and the like, and provides scientific basis for the protection, management, ecological restoration and the like of the aquatic plant.)

1. A method for constructing a solid geometric configuration of a root system of an aquatic plant is characterized by comprising the following steps of:

step (1): acquiring an aquatic plant root system image with the resolution ratio of 1:1 being more than or equal to 600dpi through a scanner;

step (2): processing the root system image in the step (1) by using root system measurement and analysis software to obtain structural data of the number of primary lateral roots, the length of the primary lateral roots, the number of secondary lateral roots, the length of the secondary lateral roots, the diameter of the secondary lateral roots, the length of a top non-branching region, the length of a tail end non-branching region, branch intervals, the number of branches, an included angle between a main root and a root hair and/or an initial growth speed of the root system;

and (3): and (3) establishing the geometric configuration of the root system according to the root system structure data obtained in the step (2).

2. The construction method according to claim 1, wherein in the step (3), the geometric configuration of the root system includes a root system elongation rule and a root system branching rule.

3. The construction method according to claim 2, wherein the root elongation rule includes a root length calculation, a root elongation rule, and an initial root growth direction.

4. The construction method according to claim 3, wherein the root length calculation: when the root age of the single root system is less than or equal to rlt, the single root system can be extended all the time, and the root system length is calculated by the formula (1):

parameter l_maxRepresenting the maximum length of the single root system, r representing the initial elongation speed of the single root system, and t being the root age of the single root system; l (t) indicates the length of the single line at time t;

root elongation rule: the single root system will elongate towards a certain direction, and the root elongation rule is described by formula (2):

the symbol G represents a root growth rule, which represents the growth change of the root after a growth interval Δ t under the conditions that the current length is l and the current time is t, and the parameter l represents the root length at t time calculated by the formula (1); delta t is the growth time interval of the root system; Δ l is the root length increment over time Δ t; r represents the growth direction of the root system; symbol F_ΔlExpressing the root segment with the length delta l, and finishing the growth of the root system with the length delta l towards the direction R through repeated iteration of a formula (2);

initial root growth direction: the initial root system growth direction R is determined by an included angle theta and a radial angle gamma of the main root and the lateral roots, wherein the included angle theta is randomly taken from normal distribution of a mean value and a standard deviation obtained by calculation of a real plant root system; the radial angle γ represents the angle of rotation of the lateral root around the main root, and is randomly chosen in a uniform distribution from 0 to 2 π.

5. The construction method according to claim 2, wherein the root branching rule is: the single root system with the branching stage number of i can generate a lateral root with the branching stage number of i +1, and the single root system is divided into three areas: area of top not branching_aTerminal unbranched region l_bAnd a branch region l_n*N，l_nThe branch distance of the single root system with the branch level number i is obtained, and N represents the maximum branch number of the single root system with the branch level number i;

when the length of the single root system is greater than the sum of the lengths of the top non-branching region and the tail non-branching region, branches can be generated, and the root length of the single root system when the single root system generates the jth branch is calculated by the formula (3):

l_j＝l_a+l_b+(j-1)*l_nformula (3)

The delay time d of the jth branch generated by the single root system can be calculated by combining the formula (1)_jComprises the following steps:

the root branching rules are described by equations (5) and (6):

B(j)->{D(0,d_j) j is less than or equal to N formula (5)

Wherein, B represents the rule generated by the root branch, the parameter j represents that the generated branch is the jth branch, B (j) represents the generation rule of the jth branch, D represents the delay rule, D is the delay time of the jth branch, and can be calculated by formula (4), D (0, D_j) Representing the elapsed delay time d of the jth branch_jThis branch then produces:

equation (6) explains the delay rule specific symbol substitution process, where t_endBy the formula (5), t_endAfter substitution is d_jIf the current time t is greater than d after the growth time interval delta t_jOr t_endA new branch B will be generated and marked as B_newThe branch B_newIs the j +1 th branch of B, and B_newStart to invoke growth rule G to start growth, B (1) denotes B_newThe 1 st branch will be generated.

6. The constructing method according to any one of claims 1 to 5, wherein the step (1): acquiring an aquatic plant root system image with the resolution of 1:1 of the root system being more than or equal to 600dpi through a scanner; and (3): and (3) establishing a geometric configuration of a root system according to the root system structure data obtained in the step (2), and then expanding the geometric configuration of the whole root system.

7. The construction method according to claim 6, characterized in that in the step (3), after the geometric configuration of one root system is established, the steps 1) -2) are repeated to establish the geometric configurations of the other root systems, and then the geometric configurations of the whole root system are combined; or after the geometric configuration of one root system is established, the method is popularized to the geometric configuration of the whole root system according to the relationship among the root systems.

Technical Field

The invention belongs to the technical field of plant simulation, and particularly relates to a method for constructing a solid geometric configuration of a root system of an aquatic plant.

Background

The evolution of the plant root system is the basis for the migration of plants from the aquatic environment to the terrestrial environment and ultimately leads to a functional division between the sugar synthesis by the leaves, the root supply (mainly water and nutrients). As one of three major vegetative organs of plants, the root system plays a critical role in the circulation of matter and energy flow in the biosphere. Root system configuration plays an important role in plant resource utilization.

The plant root system configuration refers to the shape and distribution of root systems in a growing medium, and comprises the distribution of various roots of the same root system in the medium along a two-dimensional plane of a root axis (plane geometric configuration) and the three-dimensional spatial distribution of different types of root systems in the medium, wherein the two configurations can be expressed by root system topological indexes. The research methods for plant root system configuration in recent decades can be divided into two main categories:

the first method is to obtain the real root system configuration of the plant by scanning or micro root tube method (Minirhizotron), and then analyze the root system shape and topological index by software (WinRhizo, Simroot) and the like. The method has the advantages that the obtained data is real, the continuous growth data of the root system can be obtained, and the three-dimensional geometrical configuration of the root system can be reflected by modeling the two-dimensional configuration of the root system. However, the workload of acquiring the plant root system by the excavation method is large, and the root system condition of the forest arbor can be reflected only by local excavation. The three-dimensional configuration of the root system is built through the two-dimensional configuration of the plant root system, so that the information of the part of the root system is lost inevitably. In addition, the root system model is difficult to be suitable for the root system which has already finished growing.

The second method is to carry out quantitative research on the morphological structure of the plant by constructing a model of the plant morphology and structure, summarize the growth rule of the plant, modify the plant root system configuration model according to the growth condition of the plant, and quantitatively express the morphological structure of the plant in a proper way, thereby simplifying the root system model and reducing the calculation amount. The second method is represented by an L system which is developed in recent decades and reproduces the development process of a plant root system through computer simulation, and can better simulate the growth condition of the plant. The L system was proposed by Aristid Lindenmayer in 1968 and named in his initials, and was later developed by Przemyslow Prusinkiewicz et al for growth simulation of plants and plant organs. The assumption of the method on the root system configuration of the terrestrial plant is established on the two preconditions of symmetry and self-similarity of the plant structure, namely the assumption that the geometric shape of the plant tissue structure has similarity locally and wholly, and the root system configuration model established from the two assumptions can better accord with the actual situation, and the simulation result of the leaf mosaic, stem branch and inflorescence of the plant is better. The plant local root system is used for simulating the characteristics of the whole root system, and the three-dimensional space model construction is dynamically carried out on the plant root systems such as rice under various nutrition conditions, so that the topological structure of the root system can be well characterized. However, researches show that the root system of the water plant Eichhornia crassipes (Eichhornia crassipes) can better meet the assumption of symmetry, but does not meet the assumption of self-similarity. The local root system and the whole root system of the eichhornia crassipes are structurally inconsistent, and the whole root system is a special forked branch configuration formed by a plurality of fishbone-shaped root systems and is called as a radial polymerization configuration. A similar situation was also found in another aquatic plant Pistia stratiotes. Therefore, a root system model is established in the aquatic plant, the specificity of the root system needs to be carefully considered, and the applicability of the self-similarity in the aquatic plant is discussed according to the situation.

In the conventional research methods for plant roots, a common micro-root canal method can acquire root structure information in a non-contact manner, and a large amount of research is already carried out on wheat, rice and soybean crops. However, the micro-root-canal method is only suitable for terrestrial plants, and the roots of aquatic plants are buried in a substrate full of water and cannot transmit data in real time through the micro-root-canal method, so that the research on the roots of the aquatic plants focuses more on the morphological characteristics and functional characters of the roots, the attention on the structure of the roots is relatively less, and the report of establishing a dynamic growth model by measuring the growth indexes of the roots is lacked.

Disclosure of Invention

The invention provides a method for constructing a three-dimensional geometric configuration of an aquatic plant root system, which realizes visualization of the configuration of the aquatic plant root system.

In order to solve the technical problems, the technical scheme adopted by the invention is as follows:

a method for constructing a solid geometric configuration of a root system of an aquatic plant comprises the following steps of sequentially connecting:

step (1): acquiring a 1:1 high-resolution (more than or equal to 600dpi) aquatic plant root system image through a scanner;

step (2): processing the root system image in the step (1) by using root system measurement and analysis software to obtain structural data such as the number of primary lateral roots, the length of the primary lateral roots, the number of secondary lateral roots, the length of the secondary lateral roots, the diameter of the secondary lateral roots, the length of a top non-branching region, the length of a tail end non-branching region, branch intervals, branch numbers, an included angle between a main root and a root hair and/or an initial growth speed of the root system;

and (3): and (3) establishing the geometric configuration of the root system according to the root system structure data obtained in the step (2).

The core concept of the L system is iterative replacement (rewriting), which is a method for expressing a complex object by partially or completely continuously replacing a simple initial object in an iterative process based on an iterative replacement rule, also called a production (p) rule. The L system uses characters as core and the generation rule of characters as replacement rule. The L system internally uses a character string to represent the state of the system, and the character string is called as an L character string. The initial state of the system, i.e., the initial L-string, is called axiom. The iterative substitution rule for generating the formula p is the character in the L character string. In each evolution period, the L system applies the generative formula to modify the system state (L character string) to form a new system state. Therefore, the L system finally obtains a character string consisting of specific letters, and the L system graphical description is realized by giving a specific graphical meaning to each letter in the L system. Consider a system ab consisting of only two letters a and b, assuming the resulting equations p are a → ab and b → a, i.e., a is replaced by ab and b is replaced by a. According to the rule ab is replaced by aba for the first time, replaced by abaab for the second time, replaced by abaabaabaababa for the third time, replaced by abaabaabaabaabaabaabaabaab for the fourth time, and replaced by abaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaabaaba … … for the fifth time, because the growth of the plant root system can be regarded as a continuous and repeated process, the dynamic growth process of the plant root system can be better simulated by the L system.

At present, better research is carried out on an L system established in terrestrial plants on the basis of the assumption that plant roots have symmetry and self-similarity, but at present, the research finds that the root system configuration of some aquatic plants such as Eichhornia crassipes (Eichhornia crassipes) does not accord with the L system self-similarity assumption, and the three-dimensional geometric configuration of the aquatic plant root system which does not accord with the L system self-similarity assumption is established by improving the L system.

The application can simulate the dynamic growth process of aquatic plants from seedlings to mature individuals and from simple roots to complex roots through model construction. The adaptability of the aquatic plants to the aquatic ecosystem can be explained from the aspect of root system configuration, and scientific basis can be provided for aquatic plant protection, management and ecological restoration.

In the step (3), the geometric configuration of the root system includes a root system elongation rule and a root system branch rule.

The root elongation rules include root length calculation, root elongation rules, and initial root growth direction.

Calculating the root length: when the root age of the single root system is less than or equal to the root life (rlt), the single root system can be extended all the time, and the root length is calculated by the formula (1):

parameter l_maxRepresenting the maximum length of the single root system, r representing the initial elongation speed of the single root system, and t being the root age of the single root system; l (t) indicates the length of the single line at time t;

root elongation rule: the single root system will elongate towards a certain direction, and the root elongation rule is described by formula (2):

the symbol G represents a root growth rule, which represents the growth change of the root after a growth interval Δ t under the conditions that the current length is l and the current time is t, and the parameter l represents the root length at t time calculated by the formula (1); delta t is the growth time interval of the root system; Δ l is the root length increment over time Δ t; r represents the growth direction of the root system; symbol F_ΔlDenotes the root segment of length Δ l, generalThe repeated iteration of the formula (2) can complete the growth of the root system with the length delta l towards the direction R;

initial root growth direction: the initial root system growth direction R is determined by an included angle theta and a radial angle gamma of the main root and the lateral roots, wherein the included angle theta is randomly taken from normal distribution of a mean value and a standard deviation obtained by calculation of a real plant root system; the radial angle γ represents the angle of rotation of the lateral root around the main root, and is randomly chosen in a uniform distribution from 0 to 2 π (FIG. 1). In the root system growth process, in order to enable the generated root system to have more randomness and to be more in line with the actual situation of plant growth, random angle change is added to the initial root system growth direction, random values are taken from the uniform distribution of 0 to 2 pi, namely when the root segment with the length of delta l grows, the growth scale dx of the root segment is set (dx < delta l), and then the dx length is increased according to the growth direction with the random angle change until the delta l length growth is completed.

The root system branching rules are as follows: the single root system with the branching stage number of i can generate a lateral root with the branching stage number of i +1, and the single root system is divided into three areas: apical unbranched region (l)_a) Terminal unbranched region (l)_b) And a branch region (l)_nN) (shown in fig. 2), l_nThe branch distance of the single root system with the branch level number i is obtained, and N represents the maximum branch number of the single root system with the branch level number i;

when the length of the single root system is greater than the sum of the lengths of the top non-branching region and the tail non-branching region, branches can be generated, and the root length of the single root system when the single root system generates the jth branch is calculated by the formula (3):

l_j＝l_a+l_b+(j-1)*l_nformula (3)

The delay time d of the jth branch generated by the single root system can be calculated by combining the formula (1)_jComprises the following steps:

the root branching rules are described by equations (5) and (6):

B(j)->{D(0,d_j) j is less than or equal to N formula (5)

Wherein, B represents the rule generated by the root branch, the parameter j represents that the generated branch is the jth branch, B (j) represents the generation rule of the jth branch, D represents the delay rule, D is the delay time of the jth branch, and can be calculated by formula (4), D (0, D_j) Representing the elapsed delay time d of the jth branch_jThis branch then produces:

where D represents the number of branches at time t, where t_endIs the branch end time; delta t is the growth time interval of the root system, and the formula (6) explains the specific symbol substitution process of the delay rule, wherein t is_endBy the formula (5), t_endAfter substitution is d_jIf the current time t is greater than d after the growth time interval delta t_jOr t_endA new branch B will be generated and marked as B_newThe branch B_newIs the j +1 th branch of B, and B_newStart to invoke growth rule G to start growth, B (1) denotes B_newThe 1 st branch will be generated.

As a specific implementation, step (1): acquiring a root system image of the aquatic plant with a 1:1 high resolution (more than or equal to 600dpi) of the root system through a scanner; and (3): and (3) establishing a geometric configuration of a root system according to the root system structure data obtained in the step (2), and then expanding the geometric configuration of the whole root system.

In the method, the individual root systems are cut and respectively scanned, and then the root system configuration is combined to research the real integral root system structure; or after the geometric configuration of one root system is established, the method is popularized to the geometric configuration of the whole root system according to the law among the root systems.

In the step (3), after the geometric configuration of one root system is established, repeating the steps 1) -2) to establish the geometric configurations of the other root systems, and then combining the geometric configurations of the whole root system; or after the geometric configuration of one root system is established, the method is popularized to the geometric configuration of the whole root system according to the rule between the real root systems obtained by research.

When the three-dimensional geometric configuration of the root system of the eichhornia crassipes is constructed, a model of a single root system of the eichhornia crassipes is firstly established, and the three-dimensional structure of the local root system is simulated really and then combined or popularized into the structure of the whole plant, so that the growth process of the root system of aquatic plants such as the eichhornia crassipes is simulated really.

The prior art is referred to in the art for techniques not mentioned in the present invention.

The method for constructing the three-dimensional geometric configuration of the aquatic plant root system realizes visualization of the configuration of the aquatic plant root system, can simulate the growth process of the aquatic plant root system more truly, provides a simple and intuitive tool for researching and analyzing the plasticity influence of nutrient elements around the root system on the growth and development of the aquatic plant root system, and the like, and provides scientific basis for aquatic plant protection, management, ecological restoration and the like.

Drawings

FIG. 1 is a diagram of the growth of the roots of an aquatic plant of the present invention;

FIG. 2 is a schematic diagram of a self-similar structure of the root system branches of the aquatic plants according to the present invention;

FIG. 3 is a process for visualizing the roots of aquatic plants in accordance with the present invention;

FIG. 4 is a view of the construction of the integral root system of Eichhornia crassipes, wherein 4A is a material object diagram and 4B is a construction diagram;

fig. 5 is a view of the construction of a single primary root system of eichhornia crassipes, wherein 5A is a model of the single primary root system, and 5B is a model of the single root system.

FIG. 6 is a view of the construction of the whole root system of Iphidophyllum spicatum, wherein 6A is a real object diagram and 6B is a construction diagram;

in the figure, 1 is the main root, 2 is the lateral root, 3 is the single root of the branching level i, 4 is the lateral root of the branching level i +1, and 5 is the root hair.

Detailed Description

In order to better understand the present invention, the following examples are further provided to illustrate the present invention, but the present invention is not limited to the following examples.

Example 1

The exotic invasive plants of Eichhornia crassipes, also called water hyacinth and Eichhornia crassipes, belong to floating plants in aquatic plants and are native to the Asian river basin in south America. The eichhornia crassipes is originally used as an ornamental plant and introduced into China, a continuous sheet floating vegetation mat layer is formed on the water surfaces of habitats such as rivers and lakes in the Yangtze river and south after escaping, the sunlight is shielded, the exchange of water bodies and atmosphere is prevented, and organisms such as submerged plants, fishes, mollusks and the like are killed, and the Eichhornia crassipes is listed in IUCN 100 famous world invasive species records and the first batch Chinese invasive species list (2003). The roots of the water hyacinth are very complex and overlap a lot, and the complete roots can not be obtained by the conventional scanning analysis method. The real whole root system structure is researched by a method of cutting the independent root systems to respectively scan and then combining the independent root systems into a root system configuration.

The eichhornia crassipes plants were cultured in the laboratory. After cutting off the root and stem junction of the eichhornia crassipes, the root system is placed in a transparent water tank on a scanner by using tweezers, and tap water is added until the volume of the water tank is about 2/3. And (5) unfolding the root system by using tweezers to enable the root system to be in a dispersed non-overlapping state. Typically, only one root system is scanned at a time; if the root system is small, a plurality of root systems can be scanned at one time. Root images were acquired using an epressen 12000XL scanner (Seiko Epson corp., Suwa, Nagano, Japan). The image resolution is set to 600dpi, and a 1:1 non-compressed 8-bit high-resolution tiff format image is saved after scanning. This scanner is equipped with two light sources: a white LED light source and an infrared IR light source. The method uses WinRHIO root system measurement and analysis software (Regent Instruments Inc., Quebec City, Canada) to process the root system image scanned by the scanner, and the software analyzes the root system image information by a non-statistical method to obtain the root system structure data. In order to make the root system clearly contrast with the background, 0.2 mmol.L of the nearly transparent eichhornia crassipes root system is used in advance^-1(0.075mg·mL^-1) And after dyeing for 30s, the methylene blue solution is scanned by using a white LED light source, and the background is a white background plate matched with the inner side of the scanner. The water hyacinth root system is unique, and it can be regarded that all the first-level root systems grow on one growth point (fig. 4A). The number of first-stage root systems of the water hyacinth at the final stage of growth exceeds 100, each single first-stage root system has only one main root, and a great number of main roots are densely grown on the main rootSecondary root system (fig. 4A). Based on the actual growth condition of a single first-stage root system of the eichhornia crassipes, the method is arranged in the growth period of the root system, a main root with 0 branch stage is generated every 3 days, and a model of the root system of the eichhornia crassipes can be established. Therefore, a model of a single first-level root system of Eichhornia crassipes (FIG. 5A) is first established. The geometric configuration of the whole plant root system is formed by relatively truly simulating the three-dimensional structure of a single primary root system, so that the growth process of the eichhornia crassipes is simulated more truly. The eichhornia crassipes can expand one time of population only by 12 days at least, in the example, the growth simulation of the eichhornia crassipes is carried out for 30 days, and in practice, the time is enough for the eichhornia crassipes to complete the growth process.

The single first-level root system of Eichhornia crassipes is mainly composed of a main root with the branch level of 0 and dense root hairs with the branch level of 1, wherein the root hairs do not generate branches (fig. 5A).

Parameters such as the length of a single root of the eichhornia crassipes root system, the branch distance, the non-branching region at the top end, the non-branching region at the tail end, the number of branches and the like are measured (table 1), and a model of a single root system of eichhornia crassipes can be established (fig. 5B).

The geometric configuration of the whole plant root system comprises a root system elongation rule and a root system branch rule;

the root system elongation rule comprises root system length calculation, a root elongation rule and an initial root system growth direction;

calculating the root length: when the root age of the single root system is less than or equal to the root life (rlt), the single root system can be extended all the time, and the root length is calculated by the formula (1):

parameter l_maxRepresenting the maximum length of the single root system, r representing the initial elongation speed of the single root system, and t being the root age of the single root system; l (t) indicates the length of the single line at time t;

root elongation rule: the single root system will elongate towards a certain direction, and the root elongation rule is described by formula (2):

the symbol G represents a root growth rule, which represents the growth change of the root after a growth interval Δ t under the conditions that the current length is l and the current time is t, and the parameter l represents the root length at t time calculated by the formula (1); Δ t is the growth time interval of the root system, which is set to 1 day in this study; Δ l is the root length increment over time Δ t; r represents the growth direction of the root system; symbol F_ΔlExpressing the root segment with the length delta l, and finishing the growth of the root system with the length delta l towards the direction R through repeated iteration of a formula (2);

initial root growth direction: the initial root system growth direction R is determined by an included angle theta and a radial angle gamma of the main root and the lateral roots, wherein the included angle theta is randomly taken from normal distribution of a mean value and a standard deviation obtained by calculation of a real plant root system; the radial angle γ represents the angle of rotation of the lateral root around the main root, and is randomly chosen in a uniform distribution from 0 to 2 π (shown in FIG. 1); in the root system growth process, in order to enable the generated root system to have more randomness and to be more in line with the actual situation of plant growth, random angle change is added to the initial root system growth direction, random values are taken from the uniform distribution of 0 to 2 pi, namely when the root segment with the length of delta l grows, the growth scale dx of the root segment is set (dx < delta l), and then the dx length is increased according to the growth direction with the random angle change until the delta l length growth is completed.

Root system branching rules:

the single root system with the branching stage number of i can generate a lateral root with the branching stage number of i +1, and the single root system is divided into three areas: apical unbranched region (l)_a) Terminal unbranched region (l)_b) And a branch region (l)_nN) (shown in fig. 2), l_nThe branch distance of the single root system with the branch level number i is obtained, and N represents the maximum branch number of the single root system with the branch level number i;

when the length of the single root system is greater than the sum of the lengths of the top non-branching region and the tail non-branching region, branches can be generated, and the root length of the single root system when the single root system generates the jth branch is calculated by the formula (3):

l_j＝l_a+l_b+(j-1)*l_nformula (3)

The delay time d of the jth branch generated by the single root system can be calculated by combining the formula (1)_jComprises the following steps:

the root branching rules are described by equations (5) and (6):

B(j)->{D(0,d_j) j is less than or equal to N formula (5)

Wherein, B represents the rule generated by the root branch, the parameter j represents that the generated branch is the jth branch, B (j) represents the generation rule of the jth branch, D represents the delay rule, D is the delay time of the jth branch, and can be calculated by formula (4), D (0, D_j) Representing the elapsed delay time d of the jth branch_jThis branch then produces:

equation (6) explains the delay rule specific symbol substitution process, where t_endBy the formula (5), t_endAfter substitution is d_jIf the current time t is greater than d after the growth time interval delta t_jOr t_endA new branch B will be generated and marked as B_newThe branch B_newIs the j +1 th branch of B, and B_newStart to invoke growth rule G to start growth, B (1) denotes B_newThe 1 st branch will be generated.

The plant can grow and branch by adopting a root system elongation rule G and a root system branch rule B, an initial state is set to be GB (j), wherein a value of j can be set to be 1, a single root or an initial branch can be represented, and the initial state of the root system is GB (1), and a process GB (1) - > RFGD- > RFRFRFGD- > RFRFRFRFRFRFRFRFRFRFRFRFGB (j +1) GB (1) shows a character string after three iterations, wherein the visualization process of the process is shown in figure 3, wherein symbols such as G, D, B, R and the like do not have corresponding visualization graphs, and F corresponds to a certain visualization graph (such as a line segment). GB (1) represents a new seed or initial branch, and after the first growth, GB (1) becomes RFGD, and takes values according to the included angle θ and radial angle γ included by the symbol R during visualization, thereby visually showing the root section f. after the third growth, GB (1) becomes rfrfrfrfrfrfgb (j +1) GB (1), where RFRFRF represents that the single root or branch has 3 root sections, and GB (j +1) represents that the single root will continue to grow, and generate the j +1 th branch.

Through the construction of the geometric configuration, 2,022.54m (root hair length x root hair number a x primary root system number) of the total root hair length of a mature eichhornia crassipes root system (table 2) can be calculated, and the total length of the mature root system of one eichhornia crassipes can reach astonishingly 2,042.78m by adding 20.24m (primary root length x primary root system number c) of the primary root system of the eichhornia crassipes. The geometric configuration simulates the growth process of the water hyacinth root system more truly and is consistent with the actual growth of the water hyacinth.

TABLE 1A single first-level root system model parameter for Eichhornia crassipes

TABLE 2 initial and mature root system indexes of whole Eichhornia Crassipes

Example 2

The foxtail ear flower (Myriophyllum spicatum), also known as spicate foxtail, is present in all parts of China, grows in ponds or rivers and is widely distributed in the world. The root system of the myriophyllum spicatum is in a typical forked branch configuration, and most of the root systems of aquatic plants are in the forked branch configuration, so that the root systems of the plants are selected for growth simulation construction and are representative.

Root images were acquired using an epressen 12000XL scanner (Seiko Epson corp., Suwa, Nagano, Japan). For the roots of the light-colored myriophyllum spicatum, an infrared light source is used, and the background is colorless glass matched with the inner side of the scanner. And taking out the root system after the scanning is finished, pouring out the residual water in the water tank, washing the residual root system attached in the water tank by using tap water, and then scanning the next root system in the same way.

The root system of the foxtail spicatum has the following characteristics: has robust and developed primary root systems, and each primary root system has an undeveloped secondary root system (as shown in fig. 6A). The seedling root system has 26.2 first-grade root systems on average, and the average length is 32.31mm (Table 3). The first-level lateral root of the seedling root system has 3 branches on average, and the average distance between the branches is 10.77 mm. The secondary root systems of the mature spike flower watermifoil root systems are few, about 11, and the average distance is 12.09 mm. The total length of the mature root system of the myriophyllum spicatum can be calculated to be 73.08m (the length of the primary lateral root is multiplied by the number c of the primary lateral root, the length of the secondary lateral root is multiplied by the number a of the secondary lateral root is multiplied by the number of the primary lateral root).

According to the obtained foxtail ear flower root system growth data, the foxtail ear flower root system model parameters (table 4) based on the L system are set, and the L system root system solid geometric configuration (specifically the same as the embodiment 1) is established, so that the foxtail ear flower root system growth process is simulated more truly (fig. 6B) and is consistent with the actual growth of the foxtail ear flower. The foxtail spicatus is subjected to growth simulation for 90 days, and the foxtail spicatus can grow enough to finish the growth process in practice.

TABLE 3 Whole plant emergence and mature root system index of Myriophyllum spicatum

TABLE 4 Tataria spicata root system index