New Approach to Fractal Approximation of Vector-Functions

<div>Vector-function <svg height="15.4664pt" id="M136" style="vertical-align:-3.3883pt" version="1.1" viewbox="-0.0498162 -12.0781 70.7968 15.4664" width="70.7968pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M494 439C454 435 401 429 349 428C312 446 283 454 242 454H241C152 454 48 402 48 290C48 228 85 177 146 157C127 139 95 112 44 91C43 77 48 53 58 37C73 16 92 -3 133 -18C108 -34 82 -48 58 -68C38 -84 27 -100 27 -123C27 -178 85 -244 214 -244C347 -244 481 -153 481 -39C481 66 390 84 327 84C295 84 267 82 235 82C187 81 170 103 170 120C170 131 177 140 184 148C199 146 216 143 234 143C332 143 424 195 424 299C424 333 413 356 398 376L455 371C474 382 492 414 498 432L494 439ZM235 417C284 417 305 359 305 294C305 220 284 180 245 180C198 180 176 236 176 306C176 379 205 417 235 417ZM242 -21C280 -21 302 -23 329 -29C361 -38 385 -59 385 -95C385 -148 340 -189 264 -189C185 -189 135 -141 135 -92C135 -72 144 -57 158 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id="g113-117"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="341" vert-adv-y="341"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,60.688,-5.984)"><path d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z" id="g50-52"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,65.822,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g></svg> and fractal interpolation vector-function <svg height="13.9148pt" id="M137" style="vertical-align:-3.3884pt" version="1.1" viewbox="-0.0498162 -10.5264 13.1863 13.9148" width="13.1863pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M494 439C454 435 401 429 349 428C312 446 283 454 242 454H241C152 454 48 402 48 290C48 228 85 177 146 157C127 139 95 112 44 91C43 77 48 53 58 37C73 16 92 -3 133 -18C108 -34 82 -48 58 -68C38 -84 27 -100 27 -123C27 -178 85 -244 214 -244C347 -244 481 -153 481 -39C481 66 390 84 327 84C295 84 267 82 235 82C187 81 170 103 170 120C170 131 177 140 184 148C199 146 216 143 234 143C332 143 424 195 424 299C424 333 413 356 398 376L455 371C474 382 492 414 498 432L494 439ZM235 417C284 417 305 359 305 294C305 220 284 180 245 180C198 180 176 236 176 306C176 379 205 417 235 417ZM242 -21C280 -21 302 -23 329 -29C361 -38 385 -59 385 -95C385 -148 340 -189 264 -189C185 -189 135 -141 135 -92C135 -72 144 -57 158 -42C172 -26 194 -21 242 -21Z" id="g13-101"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="492" vert-adv-y="492"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,6.747,-5.984)"><path d="M527 299L515 337L338 293L325 475H286L273 293L96 337L84 299L252 231L156 77L188 53L305 192L423 53L455 77L358 231L527 299Z" id="g50-44"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="611" vert-adv-y="611"></glyph.data></g></svg> completely identical.</div>

Abstract and Applied Analysis

New Approach to Fractal Approximation of Vector-Functions

Figure 2