[L-Systems]

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/** * @description L-systems are used to model naturally occurring patterns in nature such as growth of trees, growth of multicellular organisms, fractals etc. * by recursively applying a set of simple grammar rules over a set of variables starting with an Axiom. * @param {number} numberOfIteration - The initial string of symbols to be used as the axiom. * @param {Array<[string, string]>} condition - Array of pairs of strings (The initial string of symbols to be used as the axiom.) to be compared. Length of the array * must be not more than 2. Extra elements will be ignored. * @returns {string} - The final string of symbols after the specified number of iterations. * @ Author: Sarthak Dwivedi */ const lSystemGenerator = (numberOfIteration, condition) => { const [ruleOne, ruleTwo] = condition; let txt = ruleOne[0]; for (let i = 0; i < numberOfIteration - 1; i++) { let newTxt = ''; for (let j = 0; j < txt.length; j++) { let letter = txt.substring(j, j + 1); if (letter === ruleOne[0]) { newTxt += ruleOne[1]; } else { newTxt += ruleTwo[1]; } } txt = `${txt}\n${newTxt}`; } return txt; }; // Test case 1 - for 3 iterations console.log( lSystemGenerator(3, [ ['A', 'ABA'], ['B', 'BBB'], ]) );
Solve the following problem in your favorite programming language and send the program to us. Problem: [L-Systems]: L-systems are used to model naturally occurring patterns in nature such as growth of trees, growth of multicellular organisms, fractals etc. by recursively applying a set of simple grammar rules over a set of variables starting with an Axiom. For example: Growth of Algae in L-systems would be modelled as. variables : A B constants : none axiom : A {starting character string} rules : (A → AB), (B → A) which produces: n = 0 : S=A n = 1 : S=AB n = 2 : S=ABA n = 3 : S=ABAAB n = 4 : S=ABAABABA n = 5 : S=ABAABABAABAAB Given the upper bound ‘n’, design a class D for L-systems with variables, constants, axiom and rules. Write a function ‘produce’ that takes in the object of ‘D’ and ‘n’ as parameters and returns the L-systems string ‘S’. Tell the space and time complexity. How can you optimize your solution and what's the optimized space and time complexity?
// -Problem Statement----------
Test your program using the following L-system (Cantor fractal) where n=3 and write your answer: variables : A B constants : none start : A rules : (A → ABA), (B → BBB)
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