{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-05-26T00:16:20.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-05-26T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":44226,"title":"Logistic map","description":"The sequence defined by x_n = 4*r*x_{n-1}*(1-x_{n-1}) and a given 0 \u003c x_1 \u003c 1 turns each x_n into a polynomial of r.\r\nWrite a function f(x_1, r, n) that returns the coefficients p of this polynomial as a row vector (starting with highest degree) and the value v of this polynomial at r.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 365.5px 8px; transform-origin: 365.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe sequence defined by x_n = 4*r*x_{n-1}*(1-x_{n-1}) and a given 0 \u0026lt; x_1 \u0026lt; 1 turns each x_n into a polynomial of r.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380px 8px; transform-origin: 380px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function f(x_1, r, n) that returns the coefficients p of this polynomial as a row vector (starting with highest degree) and the value v of this polynomial at r.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [p, v] = f(x, r, n)\r\n  p = x;\r\n  v = x;\r\nend","test_suite":"%%\r\nx = 0.5;\r\nr = 0.999;\r\nn = 1;\r\nx_correct = 0.5;\r\np_correct = 0.5;\r\n[p, x] = f(x, r, n);\r\nassert(isequal(p,p_correct));\r\nassert(x==x_correct);\r\n\r\n%%\r\nx = 0.5;\r\nr = 0.999;\r\nn = 2;\r\nx_correct = 0.999;\r\np_correct = [1 0];\r\n[p, x] = f(x, r, n);\r\nassert(isequal(p,p_correct));\r\nassert(x==x_correct);\r\n\r\n%%\r\nx = 0.5;\r\nr = 0.999;\r\nn = 3;\r\nx_correct = 0.00399;\r\np_correct = [-4 4 0 0];\r\n[p, x] = f(x, r, n);\r\nassert(isequal(p,p_correct));\r\nassert(abs(x-x_correct)\u003c1E-5);\r\n\r\n%%\r\nx = 0.5;\r\nr = 0.999;\r\nn = 5;\r\nx_correct = 0.06248;\r\n[p, x] = f(x, r, n);\r\nassert(isequal(p(1:3),[-16384 65536 -98304]));\r\nassert(abs(x-x_correct)\u003c1E-5);\r\n\r\n%%\r\nx = 0.5;\r\nr = 0.999;\r\nn = 6;\r\nx_correct = 0.23407;\r\n[p, x] = f(x, r, n);\r\nassert(abs(sum(p(1:3))+2.25485E10)\u003c1E5);\r\nassert(abs(x-x_correct)\u003c1E-5);\r\n\r\n%%\r\nx = 0.5;\r\nr = 0.9999;\r\nn = 7;\r\nx_correct = 0.09891;\r\n[p, x] = f(x, r, n);\r\nassert(abs(sum(p))==4194304);\r\nassert(abs(x-x_correct)\u003c1E-5);\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":135136,"edited_by":223089,"edited_at":"2023-02-09T10:13:38.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":"2023-02-09T10:13:38.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-05-27T17:11:41.000Z","updated_at":"2026-05-25T04:54:33.000Z","published_at":"2017-05-27T17:18:57.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe sequence defined by x_n = 4*r*x_{n-1}*(1-x_{n-1}) and a given 0 \u0026lt; x_1 \u0026lt; 1 turns each x_n into a polynomial of r.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function f(x_1, r, n) that returns the coefficients p of this polynomial as a row vector (starting with highest degree) and the value v of this polynomial at r.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"problems":[{"id":44226,"title":"Logistic map","description":"The sequence defined by x_n = 4*r*x_{n-1}*(1-x_{n-1}) and a given 0 \u003c x_1 \u003c 1 turns each x_n into a polynomial of r.\r\nWrite a function f(x_1, r, n) that returns the coefficients p of this polynomial as a row vector (starting with highest degree) and the value v of this polynomial at r.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 365.5px 8px; transform-origin: 365.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe sequence defined by x_n = 4*r*x_{n-1}*(1-x_{n-1}) and a given 0 \u0026lt; x_1 \u0026lt; 1 turns each x_n into a polynomial of r.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380px 8px; transform-origin: 380px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function f(x_1, r, n) that returns the coefficients p of this polynomial as a row vector (starting with highest degree) and the value v of this polynomial at r.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [p, v] = f(x, r, n)\r\n  p = x;\r\n  v = x;\r\nend","test_suite":"%%\r\nx = 0.5;\r\nr = 0.999;\r\nn = 1;\r\nx_correct = 0.5;\r\np_correct = 0.5;\r\n[p, x] = f(x, r, n);\r\nassert(isequal(p,p_correct));\r\nassert(x==x_correct);\r\n\r\n%%\r\nx = 0.5;\r\nr = 0.999;\r\nn = 2;\r\nx_correct = 0.999;\r\np_correct = [1 0];\r\n[p, x] = f(x, r, n);\r\nassert(isequal(p,p_correct));\r\nassert(x==x_correct);\r\n\r\n%%\r\nx = 0.5;\r\nr = 0.999;\r\nn = 3;\r\nx_correct = 0.00399;\r\np_correct = [-4 4 0 0];\r\n[p, x] = f(x, r, n);\r\nassert(isequal(p,p_correct));\r\nassert(abs(x-x_correct)\u003c1E-5);\r\n\r\n%%\r\nx = 0.5;\r\nr = 0.999;\r\nn = 5;\r\nx_correct = 0.06248;\r\n[p, x] = f(x, r, n);\r\nassert(isequal(p(1:3),[-16384 65536 -98304]));\r\nassert(abs(x-x_correct)\u003c1E-5);\r\n\r\n%%\r\nx = 0.5;\r\nr = 0.999;\r\nn = 6;\r\nx_correct = 0.23407;\r\n[p, x] = f(x, r, n);\r\nassert(abs(sum(p(1:3))+2.25485E10)\u003c1E5);\r\nassert(abs(x-x_correct)\u003c1E-5);\r\n\r\n%%\r\nx = 0.5;\r\nr = 0.9999;\r\nn = 7;\r\nx_correct = 0.09891;\r\n[p, x] = f(x, r, n);\r\nassert(abs(sum(p))==4194304);\r\nassert(abs(x-x_correct)\u003c1E-5);\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":135136,"edited_by":223089,"edited_at":"2023-02-09T10:13:38.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":"2023-02-09T10:13:38.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-05-27T17:11:41.000Z","updated_at":"2026-05-25T04:54:33.000Z","published_at":"2017-05-27T17:18:57.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe sequence defined by x_n = 4*r*x_{n-1}*(1-x_{n-1}) and a given 0 \u0026lt; x_1 \u0026lt; 1 turns each x_n into a polynomial of r.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function f(x_1, r, n) that returns the coefficients p of this polynomial as a row vector (starting with highest degree) and the value v of this polynomial at r.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"errors":[],"facets":[[{"value":"Polynomials","count":1,"selected":false}],[{"value":"medium","count":1,"selected":false}]],"term":"tag:\"logistic map\"","page":1,"per_page":50,"sort":"map(difficulty_value,0,0,999) asc"}}