![]() The output of this program is an SVG file depicting a Koch snowflake. Generate Kock Curve (_SIZE_, _ITERATIONS_) Subroutine CopoNieveKoch(longitud, recursionfondo) Finish_Path ( Close_Path => True, Rendering => Fill, Rule => Even_Odd ) Doc. 3 loop Koch ( Level, Length ) Direction := Direction + 120.0 end loop Doc. Margins ( Margins_Type '( Left => Cm_2_5, others => One_cm )) Doc. To create the Koch snowflake, one would use F++F++F (an equilateral triangle) as the axiom. 7" ) Put_Line ( "open koch.pdf to view ouput" ) return end if Level := Level_Type ' Value ( Argument ( 1 )) Doc. Line ( Corner + Current ) else Koch ( Level - 1, Length / 3.0 ) Direction := Direction - 60.0 Koch ( Level - 1, Length / 3.0 ) Direction := Direction + 120.0 Koch ( Level - 1, Length / 3.0 ) Direction := Direction - 60.0 Koch ( Level - 1, Length / 3.0 ) end if end Koch begin if Argument_Count /= 1 then Put_Line ( "koch_curve " ) Put_Line ( " 0. ![]() 7 Purple : constant Color_Type := ( 0.7, 0.0, 0.5 ) Length : constant Real := 400.0 Corner : constant Point := ( 90.0, 580.0 ) Level : Level_Type Current : Point := ( 0.0, 0.0 ) Direction : Angle_Deg := Angle_Deg '( 60.0 ) Doc : PDF_Out_File procedure Koch ( Level : Level_Type Length : Real ) is begin if Level = 0 then Current := Current + Length * Point '( Sin ( Direction, 360.0 ), Cos ( Direction, 360.0 )) Doc. Text_IO subtype Angle_Deg is Real type Level_Type is range 0. With Ada.Command_Line with _Elementary_Functions with Ada.Text_IO with PDF_Out procedure Koch_Curve is package Real_Math is new _Elementary_Functions (PDF_Out.Real ) use Real_Math, PDF_Out, Ada. PROC DrawKoch(INT x,y REAL POINTER len BYTE depth) Referenced on Wolfram|Alpha Koch Snowflake Cite this as: Penguin Dictionary of Curious and Interesting Geometry. In "The On-Line Encyclopedia of Integer Sequences." Wagon, "A Generalization of the Von Koch Curves." Math. "The von Koch Snowflake Curve Revisited." §C.2 ChaosĪnd Fractals: New Frontiers of Science. "ModulusĮndlessly Repeated Geometric Figures. Pour l'étude de certaines questions de la théorie des courbes planes."Īcta Math. Tangente, obtenue par une construction géométrique élémentaire."Īrchiv för Matemat., Astron. Code Issues Pull requests Computer Graphics Project 1 opengl graphics koch-snowflake Updated on C++ grypesc / KochFractals Star 1 Code Issues Pull requests Low level combination of C and x86/圆4 assembly code that turns a curve entered by the user into a Koch's fractal. "Einheitliche Erzeugung und Darstellungĭer Kurven von Peano, Osgood und v. Koch." Arch. Of Mathematics and Computational Science. New York: Penguin Books, p. 99 and center plate Sixth Book of Mathematical Games from Scientific American. ReprintedĪs §228 in Opere scelte, a cura dell'Unione matematica italiana e col contributoĭel Consiglio nazionale delle ricerche, Vol. 2: Geometria, analisi, fisica matematica. "Remarques sur la courbe de von Koch." Atti della R. Of the initial triangle, and the length of an initial side 1. The snowflake's area after the th iteration. Iterations of the Koch snowflake is implemented in the Wolframīe the length of a single side, be the length of the perimeter, The fractal can also be constructed using a base curve and motif, illustrated above. The zeroth through third iterationsĮach fractalized side of the triangle is sometimes known as a Koch curve. Rewriting rule "F" -> "F+F-F+F", and angle. System with initial string "F-F-F", string The Koch snowflake can be simply encoded as a Lindenmayer Triangle at the location where the side was removed, and then repeating the process Removing the inner third of each side, building another equilateral It is builtīy starting with an equilateral triangle, The Koch snowflake is a fractal curve, also known as the Koch island, which was first described by Helge von Koch in 1904.
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