A fibonacci sequence based spiral tree generation demonstration system

Abstract

The application discloses a spiral tree generation demonstration system based on a Fibonacci sequence and belongs to the technical field of plant growth simulation and biological information modeling; the system comprises a cuboid wood block, a split rotary shaft, a direction instrument and a rotary control system; the application constructs a system for simulating the growth change of plant morphology through each component unit; the split rotary shaft, the direction instrument and the rotary control system control the rotary simulation of the growth change process of the morphology of the wood blocks stacked together; in the process, users can more intuitively observe the growth change of plants, can more quickly understand the advantages of plant growth based on the Fibonacci sequence by consulting data, can improve interest and can quickly master corresponding knowledge.

Description

Technical Field

[0001] This invention relates to the field of plant growth simulation and bioinformatics modeling technology, and more specifically, to a spiral tree generation demonstration system based on Fibonacci sequences. Background Technology

[0002] Plants exhibit many astonishing morphological features in nature, among which the Fibonacci sequence and spiral structure are the most representative. The Fibonacci sequence and the golden ratio are widely used in plant growth patterns. For example, the distribution of leaves, the number of petals, and the arrangement of fruits all show patterns that conform to the Fibonacci sequence. These growth characteristics are not only the result of natural selection, but are also closely related to factors such as plant growth efficiency, light exposure, and water absorption. For example, the seed distribution of sunflowers, the scale arrangement of pine cones, and the spiral structure of coconut shells all show traces of the Fibonacci sequence. The biological principles behind these phenomena profoundly influence the morphological evolution of plants and are an important topic of research in botany and biology.

[0003] However, in reality, studying the characteristics of Fibonacci sequences and helical structures in plant growth through physical experiments often faces difficulties. On the one hand, plant growth is a slow and complex process, making it difficult to observe its complete growth changes through short-term experiments. On the other hand, different plant varieties and growth environments may lead to differences in their morphological changes, making it difficult for researchers to unify the observation results under experimental conditions. In order to intuitively demonstrate and study these growth characteristics, traditional plant morphology simulation usually relies on static models and diagrams, which cannot dynamically reproduce the changes in the plant growth process.

[0004] Most existing models and experimental methods rely on a single physical structure or two-dimensional image. These static displays cannot truly reflect the changes in plant growth and the mathematical laws behind them, and it is difficult to show the advantages of plants choosing the Fibonacci sequence for growth. Simulating the dynamic process of plant growth through physical models can provide researchers with a more intuitive and flexible way of displaying the process. However, traditional simulation equipment is usually more complex and costly, and it is difficult to accurately control the simulated growth angle and pattern. Summary of the Invention

[0005] The purpose of this invention is to overcome the above-mentioned problems existing in the prior art and to greatly improve its technical effect on the basis of the original technology; to this end, this invention provides a demonstration system for generating spiral trees based on Fibonacci sequences, the system comprising: Rectangular wooden block, split rotating shaft, steering instrument and rotation control system.

[0006] The system includes multiple cuboid wooden blocks with the same width and height but different lengths; holes are drilled at the center of the plane formed by the length and width of each cuboid wooden block to form circular holes along the height direction; the circular holes of all the cuboid wooden blocks are aligned to form a circular hole channel, and all the cuboid wooden blocks are stacked in order of decreasing length from bottom to top; the cuboid wooden blocks are used to simulate plant leaves.

[0007] The length-to-width ratio L1 of the cuboid wooden blocks is set to: 2≤L1≤10, and the width-to-height ratio L2 is set to: L2≥5; the stacking of all cuboid wooden blocks in a manner that decreases in length from bottom to top includes: there are gaps between adjacent stacked cuboid wooden blocks; the cuboid wooden blocks are used to simulate plant leaves, including: the length, width, and height of the cuboid wooden blocks respectively simulate the length, width, and height of plant leaves, and cuboid wooden blocks of different lengths are used to simulate plant leaves of corresponding lengths; a keyway is reserved near the ground edge of the circular hole of each cuboid wooden block for fixing with the corresponding sub-shaft segment.

[0008] The system's split rotating shaft is composed of multiple independently rotatable sub-shaft segments coaxially connected; the split rotating shaft passes through a circular hole channel and is fixedly connected to a corresponding cuboid wooden block through each independent sub-shaft segment; it is used to control the rotation direction and angle of each cuboid wooden block to simulate the morphological changes of plant growth.

[0009] Each sub-shaft segment in the split rotating shaft is a cylindrical structure of the same length. The end faces of two adjacent sub-shaft segments are respectively provided with bearing seats and sliding joints. One sub-shaft segment has a bearing seat at its end and a bearing is installed thereon, while the other sub-shaft segment has a sliding joint at its end and is inserted into the bearing. This allows the adjacent sub-shaft segments to be coaxially connected and to rotate independently of each other. A protruding key shaft is reserved at the near-ground edge of the sub-shaft segment. The key shaft is inserted into the keyway reserved in the corresponding cuboid wooden block to fix each sub-shaft segment and the corresponding cuboid wooden block.

[0010] The system's steering instrument is connected to both the split-type rotating shaft and the rotation control system. It integrates the rotation angle of each sub-shaft segment and feeds the integrated rotation angle back to the rotation control system. Each sub-shaft segment of the split-type rotating shaft is connected to an independent motor and an angle sensor. The motor is connected to the rotation control system, and the angle sensor is connected to the steering instrument. The steering instrument acquires and integrates the rotation angle of each sub-shaft segment through the connected angle sensor and feeds the integrated information back to the rotation control system. The rotation control system ensures the rotation angle of each sub-shaft segment.

[0011] The rotation control system of the system is electrically connected to each sub-shaft segment of the directional instrument and the split rotating shaft. It is used to read the overall rotation angle of the split rotating shaft displayed by the directional instrument and trigger the drive unit of the corresponding sub-shaft segment in order from top to bottom to simulate the spiral growth characteristics of plant leaves along the stem in the Fibonacci sequence.

[0012] The rotation control system is configured as follows: S1, the sub-axis segments from top to bottom are defined as A1 to An, where A1 represents the topmost sub-axis segment and An represents the nth sub-axis segment from top to bottom; S2, after determining the angle difference α between two adjacent sub-axis segments through input commands, the rotation control system starts the rotation of the first sub-axis segment, thereby driving the rotation of the corresponding cuboid wooden block. 0 <α≤180 0 S3, When the rotation angle of the first sub-shaft segment reaches a distance of α and β, start the rotation of the second sub-shaft segment, so that the total rotation angle difference between the first and second sub-shaft segments remains at α, and the first and second sub-shaft segments maintain uniform rotation; S4, When the rotation angle of the second sub-shaft segment reaches a distance of α and β, start the rotation of the third sub-shaft segment, so that the total rotation angle difference between the second and third sub-shaft segments remains at α, and the second and third sub-shaft segments maintain uniform rotation; S5, Following steps S3 and S4, start the rotation of the fourth to the (n-1)th sub-shaft segments in sequence, until the rotation angle of the (n-1)th sub-shaft segment reaches α, at which point all sub-shaft segments stop rotating simultaneously.

[0013] Sub-shaft segment from 0 0 The rotation to a final stop involves acceleration, constant speed, and deceleration; after the rotation control system is activated with the rotation command, each sub-shaft segment starts from 0... 0 The time from uniform rotation to accelerated rotation is T1, and the angle of acceleration is γ1. After the rotation control system initiates the stop command, the angle of deceleration from uniform rotation to stop for each sub-shaft segment is γ2. The times from the first sub-shaft segment to the (n-1)th sub-shaft segment being in uniform rotation are t1, t2, ..., t... n-1 Let θ be the velocity of each sub-shaft segment rotating at a constant speed. Then, from the first sub-shaft segment to the nth sub-shaft segment, the relationship between the physical quantities of each sub-shaft segment can be expressed by the formula. This indicates that i refers to the i-th sub-shaft segment, and the value of i is an integer from 1 to n-1; that is, the total rotation angle of each sub-shaft segment is (ni)α. When the total rotation angle of the i-th sub-shaft segment is still γ2 away from the angle (ni)α, the corresponding sub-shaft segment's stop rotation command is initiated; the formula for calculating the angle β is: .

[0014] The system's rotation control system is also equipped with a rotation angle fine-tuning program. This program is used to fine-tune the angles of uniformly rotating sub-shaft segments, ensuring that the angle difference between any two adjacent sub-shaft segments remains at α. The rotation angle fine-tuning program is configured to: continuously acquire the rotation angle of each sub-shaft segment using a direction finder; calculate whether the angle difference between the upper and lower sub-shaft segments during uniform rotation is α; if the angle difference is α, then neither of the corresponding sub-shaft segments requires fine-tuning. If the difference between the rotation angle of the upper sub-shaft segment and the rotation angle of the lower sub-shaft segment is less than α, then the rotation speed of the lower sub-shaft segment is appropriately reduced until the difference between the rotation angles of the upper and lower sub-shaft segments is α and the rotation speed of the lower sub-shaft segment is θ, at which point the fine adjustment is completed. If the difference between the rotation angles of the upper and lower sub-shaft segments is greater than α, then the rotation speed of the lower sub-shaft segment is appropriately increased until the difference between the rotation angles of the upper and lower sub-shaft segments is α and the rotation speed of the lower sub-shaft segment is θ, at which point the fine adjustment is completed.

[0015] The beneficial effects of this invention are as follows: 1) This invention uses multiple stacked wooden blocks of gradually decreasing size from bottom to top, and simulates the layered growth of plant leaves through their shape and structure. This makes the entire device structurally close to the actual phyllotaxis of plants, thus intuitively reflecting the spatial hierarchy of plant morphology and improving the biomimicry and intuitiveness of the model; 2) This invention adopts a split rotating shaft structure, with each sub-shaft segment fixedly connected to a corresponding wooden block, allowing each layer of wooden blocks to rotate independently around the axis. Through this structural design, the process of plants gradually forming phyllotaxis at different growth stages can be simulated, enabling the model to dynamically display the process of plant morphology gradually evolving into a spiral structure, and intuitively demonstrating the plant's selection of the Fibonacci sequence. Advantages; 3) By setting up a direction indicator and a rotation control system, this invention achieves real-time monitoring and feedback control of the overall rotation angle of all sub-axis segments; when the overall rotation of the split rotating shaft reaches a predetermined angle, the control system can trigger the drive units of each sub-axis segment in sequence from top to bottom, so that the corresponding wooden blocks rotate independently in sequence, thereby forming a regular spatial arrangement structure; through this angle triggering mechanism, the regular changes of gradual rotation during the formation of plant leaf sequence can be simulated more accurately; 4) The invention provides a rotation control algorithm for controlling the rotation of each sub-axis segment by the rotation control system, and provides the corresponding fine-tuning process to ensure that the rotation angle difference between two adjacent sub-axis segments is α. Therefore, it can accurately control the simulated growth angle and pattern. Attached Figure Description

[0016] Figure 1 This is a schematic diagram showing the connections of the components of the system of the present invention.

[0017] Figure 2 This is a schematic diagram illustrating a spiral tree generation demonstration system based on Fibonacci sequences according to the present invention. Detailed Implementation

[0018] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings; it should be understood that the specific embodiments given herein are only for illustration and explanation of the present invention and cannot be used to limit the present invention.

[0019] like Figure 1 The diagram shown is a schematic diagram of the connection of various components of the system according to the present invention. The schematic diagram includes: a rotation control system, a steering instrument, a combination of cuboid wooden block 1 and sub-shaft segment A1, a combination of cuboid wooden block 2 and sub-shaft segment A2, ..., and a combination of cuboid wooden block n and sub-shaft segment An.

[0020] The system connection of this invention includes the connection of a cuboid wooden block, a split rotating shaft, a steering instrument, and a rotation control system. The combination of the cuboid wooden block n and the sub-shaft segment An refers to the fastener formed by connecting the cuboid wooden block n and the sub-shaft segment An. The first fastener is connected to the second fastener, the second fastener is connected to the third fastener, and so on until the (n-1)th fastener is connected to the nth fastener. Subsequently, the rotation control system is connected to the steering instrument and to all the fasteners, specifically to each sub-shaft segment in the fasteners. Finally, the steering instrument is connected to each sub-shaft segment in the fasteners.

[0021] The following embodiments will provide a detailed description of the connection and simulation methods of this system: The present invention comprises multiple cuboid wooden blocks with the same width and height but different lengths; at the center of the plane formed by the length and width of the cuboid wooden blocks, holes are drilled along the height direction to form circular holes; the circular holes of all the cuboid wooden blocks are aligned to form a circular hole channel, and all the cuboid wooden blocks are stacked in a manner that decreases in length from bottom to top; the cuboid wooden blocks are used to simulate plant leaves.

[0022] Specifically, the ratio of the length to the width of the cuboid wooden block, L1, is set to: 2≤L1≤10, and the ratio of the width to the height, L2, is set to: L2≥5; the stacking of all cuboid wooden blocks in a manner that decreases in length from bottom to top includes: there are gaps between adjacent stacked cuboid wooden blocks; the cuboid wooden blocks are used to simulate plant leaves, including: the length, width, and height of the cuboid wooden blocks respectively simulate the length, width, and height of plant leaves, and cuboid wooden blocks of different lengths are used to simulate plant leaves of corresponding lengths; a keyway is reserved near the ground edge of the circular hole of each cuboid wooden block for fixing with the corresponding sub-shaft segment.

[0023] It should be noted that the length-to-width ratio L1 of the cuboid block is set to 2≤L1≤10 because the length-to-width ratio of most plant leaves is between 1:1 and 5:1. Setting L1 to 2≤L1≤10 ensures that the length-to-width ratio of the cuboid block perfectly matches the actual dimensions of plant leaves. The width-to-height ratio L2 is set to L2≥5 because the width of a plant is often much greater than its thickness, with the thickness equivalent to the height of the cuboid block. However, due to practical considerations and the actual need for connection to the spindle segment, the actual height of the cuboid block is designed to be L2≥5. This makes the length and width of the cuboid block significantly greater than its height, mimicking the actual height of plant leaves. However, it is important to note that the height L2 cannot be designed to be extremely small like the actual length of plant leaves; sufficient space must be left for the groove to be fixed to the spindle segment.

[0024] In addition, there are gaps between the stacked adjacent cuboid blocks; the length, width, and height of the cuboid blocks simulate the length, width, and height of plant leaves, respectively, and cuboid blocks of different lengths are used to simulate plant leaves of corresponding lengths, specifically simulating plant leaves from bottom to top; a keyway is reserved near the ground edge of the circular hole of each cuboid block for fixing with the corresponding sub-shaft segment; the existence of the reserved keyway limits the gaps between adjacent cuboid blocks, and the gaps are generally not large; however, in actual design, the gaps between adjacent cuboid blocks can be appropriately increased by increasing the length of each sub-shaft segment of the split rotating shaft.

[0025] The split-type rotating shaft of the present invention is composed of multiple independently rotatable sub-shaft segments coaxially connected; the split-type rotating shaft passes through the circular hole channel formed by the cuboid wooden block, and is fixedly connected to a corresponding cuboid wooden block through each independent sub-shaft segment; the split-type rotating shaft is used to control the rotation direction and angle of each cuboid wooden block to simulate the morphological changes of plant growth.

[0026] Each sub-shaft segment of the split rotating shaft is a cylindrical structure of equal length. Bearing seats and sliding joints are respectively provided on the end faces of adjacent sub-shaft segments. One sub-shaft segment has a bearing seat at its end and a bearing installed thereon, while the other sub-shaft segment has a sliding joint at its end that inserts into the bearing of the adjacent sub-shaft segment, thus enabling the adjacent sub-shaft segments to be coaxially connected and able to rotate independently. A protruding key shaft is reserved near the ground edge of each sub-shaft segment. This key shaft is inserted into a pre-reserved keyway in the corresponding cuboid wooden block to fix each sub-shaft segment to the corresponding cuboid wooden block. The operation of fixing each sub-axis segment and its corresponding cuboid block is as follows: First, select any sub-axis segment and place it vertically. Connect the longest cuboid block to the key shaft of the sub-axis segment through a keyway to form the bottom layer of leaves of the simulated plant. Then, connect the sub-axis segment to any other remaining sub-axis segment, and select the second longest cuboid block to fix it to the sub-axis segment to form the second layer of leaves of the simulated plant. Continue to fix all the remaining sub-axis segments and cuboid blocks in this way to complete the shape fixation of the entire plant.

[0027] The system's steering gear is connected to both a split-type rotating shaft and a rotation control system. It integrates the rotation angle of each sub-shaft segment and feeds the integrated rotation angle back to the rotation control system. Specifically, each sub-shaft segment is connected to an independent motor and an angle sensor, and is connected to the rotation control system via the motor and the steering gear via the angle sensor. The steering gear acquires and integrates the rotation angle of each sub-shaft segment through the connected angle sensor and feeds the integrated information back to the rotation control system, which then controls the rotation angle of each sub-shaft segment.

[0028] The rotation control system of the system is electrically connected to each sub-shaft segment of the directional instrument and the split rotating shaft. It is used to read the overall rotation angle of the split rotating shaft displayed by the directional instrument and trigger the drive unit of the corresponding sub-shaft segment in order from top to bottom to simulate the spiral growth characteristics of plant leaves along the stem in the Fibonacci sequence.

[0029] The rotation control system is configured as follows: S1, the sub-axis segments from top to bottom are defined as A1 to An, where A1 represents the topmost sub-axis segment and An represents the nth sub-axis segment from top to bottom; S2, after determining the angle difference α between two adjacent sub-axis segments through input commands, the rotation control system starts the rotation of the first sub-axis segment, thereby driving the rotation of the corresponding cuboid wooden block. 0 <α≤180 0S3, When the rotation angle of the first sub-shaft segment reaches a distance of α and β, start the rotation of the second sub-shaft segment, so that the total rotation angle difference between the first and second sub-shaft segments remains at α, and the first and second sub-shaft segments maintain uniform rotation; S4, When the rotation angle of the second sub-shaft segment reaches a distance of α and β, start the rotation of the third sub-shaft segment, so that the total rotation angle difference between the second and third sub-shaft segments remains at α, and the second and third sub-shaft segments maintain uniform rotation; S5, Following steps S3 and S4, start the rotation of the fourth to the (n-1)th sub-shaft segments in sequence, until the rotation angle of the (n-1)th sub-shaft segment reaches α, at which point all sub-shaft segments stop rotating simultaneously; It should be noted that the reason for not starting the rotation of the bottommost sub-shaft segment is that when the rotation angle of the (n-1)th sub-shaft segment reaches α, the requirement of the angle difference of α between all adjacent sub-shaft segments is met, therefore, it is not necessary to start the rotation of the bottommost sub-shaft segment.

[0030] The Fibonacci sequence is a widely existing sequence in mathematics and nature, characterized by F... m =F m-1 +F m-2 ;where F m For the m-th term, F m-1 This is the (m-1)th term, where m is an integer greater than 2. The Fibonacci sequence is: 1, 1, 2, 3, 5, 8, 13, ... This pattern continues in a loop, meaning the value of each subsequent term is equal to the sum of the values ​​of the two preceding terms. Plant growth in nature exhibits many mathematical patterns related to the Fibonacci sequence. For example, the number of spirals in sunflower seeds is often 34 and 55, or 55 and 89; the number of spirals in pine cone scales is often 5 and 8; and the number of spirals in pineapple eye cells is often 8, 13, and 21. The Fibonacci sequence in plant growth is not only reflected in the number of spirals but also in the arrangement of phyllotaxis, where the angle between adjacent phyllotaxis is often approximately 137.5 degrees. 0 The process of finding the golden angle is directly related to the Fibonacci sequence. The process is as follows: as the Fibonacci sequence increases, the ratio of adjacent terms gradually approaches a constant of 1.6180339887. The reciprocal of this constant is 0.618. The ratio of the golden angle obtained through this reciprocal is 1 - 0.618 = 0.382. Therefore, the golden angle 360° in a circle can be found using this ratio. 0 ×0.382=137.5 0 Therefore, the angular difference between the rotations of two adjacent cuboid wooden blocks in this system, simulating plant growth, is 137.5 degrees. 0 Therefore, the optimal value for α is 137.5. 0 .

[0031] Sub-shaft segment from 0 0 The rotation to a final stop involves acceleration, constant speed, and deceleration; after the rotation control system is activated with the rotation command, each sub-shaft segment starts from 0... 0 The time from uniform rotation to accelerated rotation is T1, and the angle of acceleration is γ1. After the rotation control system initiates the stop command, the angle of deceleration from uniform rotation to stop for each sub-shaft segment is γ2. The times from the first sub-shaft segment to the (n-1)th sub-shaft segment being in uniform rotation are t1, t2, ..., t... n-1 Let θ be the velocity of each sub-shaft segment rotating at a constant speed. Then, from the first sub-shaft segment to the nth sub-shaft segment, the relationship between the physical quantities of each sub-shaft segment can be expressed by the formula. This indicates that i refers to the i-th sub-shaft segment, and the value of i is an integer from 1 to n-1; that is, the total rotation angle of each sub-shaft segment is (ni)α. When the total rotation angle of the i-th sub-shaft segment is still γ2 degrees away from the angle (ni)α, the corresponding sub-shaft segment's stop rotation command is initiated; the formula for calculating angle β is: This setting ensures that when all sub-shaft segments stop rotating, the included angle between any two adjacent sub-shaft segments is α.

[0032] In addition, to further ensure that the included angle between any two adjacent sub-shaft segments is α after all sub-shaft segments have stopped rotating, the rotation control system is also equipped with a rotation angle fine-tuning program. This program is used to fine-tune the angles of uniformly rotating sub-shaft segments, maintaining the angle difference between any two adjacent sub-shaft segments at α. The rotation angle fine-tuning program is configured to: continuously acquire the rotation angle of each sub-shaft segment using a direction finder; calculate whether the difference between the rotation angles of adjacent upper and lower sub-shaft segments during uniform rotation is α; if the difference is α... If the difference between the rotation angles of the upper and lower sub-shaft segments is less than α, then the rotation speed of the lower sub-shaft segment should be appropriately reduced until the difference between the rotation angles of the upper and lower sub-shaft segments is α and the rotation speed of the lower sub-shaft segment is θ, at which point the fine-tuning is complete. If the difference between the rotation angles of the upper and lower sub-shaft segments is greater than α, then the rotation speed of the lower sub-shaft segment should be appropriately increased until the difference between the rotation angles of the upper and lower sub-shaft segments is α and the rotation speed of the lower sub-shaft segment is θ, at which point the fine-tuning is complete.

[0033] like Figure 2The diagram illustrates a demonstration system for generating a spiral tree based on the Fibonacci sequence, as presented in this invention. The diagram shows that the rectangular wooden block, after rotation, exhibits a spiral structure, significantly increasing its contact area with its surroundings. The system includes a rectangular wooden block, a split-type rotating shaft, a directional sensor, and a rotation control system. The split-type rotating shaft, serving as the rotational support for the rectangular wooden block, is concealed at its central axis by the block. The directional sensor and rotation control system are integrated within a green cylindrical structure. Different angle values ​​α can be selected using the buttons of this invention, causing all adjacent rectangular wooden blocks to exhibit a spiral structure with an angle difference of α. To clearly observe the spiral structure, the value of α can be gradually increased from a small value, observing the spiral structure exhibited by different angle differences α. Simultaneously, by illuminating the system from different directions at different angle values, the system simulates the sunlight exposure of plants throughout the day. The system is then analyzed to determine at what angle α the rectangular wooden block receives the maximum total area of ​​light throughout the illumination process. Verification shows that when the α value is approximately 137.5... 0 At that time, the total area of ​​light received by the rectangular wooden block was the largest; this further verified the advantage of the plant growth exhibiting the Fibonacci sequence growth and the golden angle between the leaf arrangement.

Claims

1. A demonstration system for generating spiral trees based on Fibonacci sequences, characterized in that, The system includes: Rectangular wooden block, split rotating shaft, steering instrument and rotation control system; The cuboid wooden block comprises: multiple cuboid wooden blocks with the same width and height but different lengths; at the center of the plane formed by the length and width of the cuboid wooden blocks, holes are drilled along the height direction to form circular holes; the circular holes of all the cuboid wooden blocks are aligned to form a circular hole channel, and all the cuboid wooden blocks are stacked in a manner that decreases in length from bottom to top; the cuboid wooden blocks are used to simulate plant leaves; The split-type rotating shaft comprises: multiple independently rotatable sub-shaft segments coaxially connected; the split-type rotating shaft passes through the circular hole channel and is fixedly connected to a corresponding cuboid wooden block through each independent sub-shaft segment; the split-type rotating shaft is used to control the rotation direction and angle of each cuboid wooden block to simulate the morphological changes of plant growth; The direction indicator includes: a split rotating shaft and a rotation control system respectively, used to integrate the rotation angle of each sub-shaft segment and feed the integrated rotation angle back to the rotation control system; The rotation control system includes: the rotation control system is electrically connected to each sub-shaft segment of the directional instrument and the split-type rotation shaft respectively; it is used to read the overall rotation angle of the split-type rotation shaft displayed by the directional instrument, and sequentially trigger the drive units of the corresponding sub-shaft segments in order from top to bottom, to simulate the spiral growth characteristics of plant leaves along the stem in the Fibonacci sequence.

2. The spiral tree generation demonstration system based on Fibonacci sequences according to claim 1, characterized in that, The length-to-width ratio L1 of the cuboid wooden block is set to: 2≤L1≤10, and the width-to-height ratio L2 is set to: L2≥5; stacking all the cuboid wooden blocks in a manner that decreases in length from bottom to top includes: there are gaps between adjacent stacked cuboid wooden blocks; the cuboid wooden blocks are used to simulate plant leaves, including: the length, width, and height of the cuboid wooden blocks simulate the length, width, and height of plant leaves, respectively, and cuboid wooden blocks of different lengths are used to simulate plant leaves of corresponding lengths; a keyway is reserved near the ground edge of the circular hole of each cuboid wooden block for fixing with the corresponding sub-shaft segment.

3. The spiral tree generation demonstration system based on Fibonacci sequences according to claim 1, characterized in that, The split-type rotating shaft includes: each sub-shaft segment is a cylindrical structure of the same length, and the end faces of two adjacent sub-shaft segments are respectively provided with bearing seats and sliding joints. One sub-shaft segment has a bearing seat at its end and a bearing is installed thereon, while the other sub-shaft segment has a sliding joint at its end and is inserted into the bearing, so that the adjacent sub-shaft segments are coaxially connected and can rotate independently of each other; a protruding key shaft is reserved at the near-ground edge of the sub-shaft segment, and the key shaft is inserted into the keyway reserved in the corresponding cuboid wooden block to fix each sub-shaft segment and the corresponding cuboid wooden block.

4. The spiral tree generation demonstration system based on Fibonacci sequences according to claim 1, characterized in that, The steering system includes: each sub-shaft segment is connected to an independent motor and an angle sensor, and is connected to the rotation control system through the motor and the steering system through the angle sensor; the steering system acquires and integrates the rotation angle of each sub-shaft segment through the connected angle sensor, and feeds the integrated information back to the rotation control system, which ensures the rotation angle of each sub-shaft segment.

5. The spiral tree generation demonstration system based on Fibonacci sequences according to claim 1, characterized in that, The rotation control system is configured as follows: S1, the sub-shaft segments from top to bottom are defined as A1 to An, where A1 represents the topmost sub-shaft segment and An represents the nth sub-shaft segment from top to bottom; S2, after determining the angle difference α between two adjacent sub-shaft segments through input instructions, the rotation control system starts the rotation of the first sub-shaft segment, thereby driving the rotation of the corresponding cuboid wooden block. 0 <α≤180 0 S3, When the rotation angle of the first sub-shaft segment reaches a distance of α and β, start the rotation of the second sub-shaft segment, so that the total rotation angle difference between the first and second sub-shaft segments remains at α, and the first and second sub-shaft segments maintain uniform rotation; S4, When the rotation angle of the second sub-shaft segment reaches a distance of α and β, start the rotation of the third sub-shaft segment, so that the total rotation angle difference between the second and third sub-shaft segments remains at α, and the second and third sub-shaft segments maintain uniform rotation; S5, Following steps S3 and S4, start the rotation of the fourth to the (n-1)th sub-shaft segments in sequence, until the rotation angle of the (n-1)th sub-shaft segment reaches α, at which point all sub-shaft segments stop rotating simultaneously.

6. The spiral tree generation demonstration system based on Fibonacci sequences according to claim 5, characterized in that, The sub-shaft segment starts from 0 0 The rotation to a final stop involves acceleration, constant speed, and deceleration; after the rotation control system is activated with the rotation command, each sub-shaft segment starts from 0... 0 The time from uniform rotation to accelerated rotation is T1, and the angle of acceleration is γ1. After the rotation control system initiates the stop command, the angle of deceleration from uniform rotation to stop for each sub-shaft segment is γ2. The times from the first sub-shaft segment to the (n-1)th sub-shaft segment being in uniform rotation are t1, t2, ..., t... n -1, the velocity of each sub-shaft segment rotating at a uniform speed is θ; then the relationship between the physical quantities of each sub-shaft segment from the first sub-shaft segment to the nth sub-shaft segment is expressed by the formula. This indicates that i refers to the i-th sub-shaft segment, and the value of i is an integer from 1 to n-1; that is, the total rotation angle of each sub-shaft segment is (ni)α. When the total rotation angle of the i-th sub-shaft segment is still γ2 away from the angle (ni)α, the corresponding sub-shaft segment's stop rotation command is initiated; the formula for calculating the angle β is: .

7. The spiral tree generation demonstration system based on Fibonacci sequences according to claim 1, characterized in that, The rotation control system is also equipped with a rotation angle fine-tuning program, which is used to fine-tune the angle of uniformly rotating sub-shaft segments so that the angle difference between any two adjacent sub-shaft segments is maintained at α. The rotation angle fine-tuning program is configured to: continuously acquire the rotation angle of each sub-shaft segment through a direction instrument, and calculate whether the difference between the rotation angle of the adjacent upper sub-shaft segment and the rotation angle of the lower sub-shaft segment during uniform rotation is α; if the difference between the rotation angle of the upper sub-shaft segment and the rotation angle of the lower sub-shaft segment is α, then neither of the two corresponding sub-shaft segments needs to be fine-tuned. If the difference between the rotation angle of the upper sub-shaft segment and the rotation angle of the lower sub-shaft segment is less than α, then the rotation speed of the lower sub-shaft segment is appropriately reduced until the difference between the rotation angles of the upper and lower sub-shaft segments is α and the rotation speed of the lower sub-shaft segment is θ, at which point the fine adjustment is completed. If the difference between the rotation angles of the upper and lower sub-shaft segments is greater than α, then the rotation speed of the lower sub-shaft segment is appropriately increased until the difference between the rotation angles of the upper and lower sub-shaft segments is α and the rotation speed of the lower sub-shaft segment is θ, at which point the fine adjustment is completed.

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