Julia and Mandelbrot Sets of Transcendental Function via Fibonacci-Mann Iteration

<div>Effect of change in parameters <svg height="10.643pt" id="M281" style="vertical-align:-1.576489pt" version="1.1" viewbox="-0.0498162 -9.06651 21.3038 10.643" width="21.3038pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M607 133C586 112 562 92 536 78C517 67 496 58 474 58C435 58 384 81 341 101C371 128 400 156 424 189C438 209 453 230 453 255C453 275 443 292 434 309C418 335 399 360 378 383C366 397 355 411 347 427C341 438 336 450 336 463C336 486 347 506 360 524C378 549 401 568 426 585C463 579 500 574 538 575C562 576 586 578 607 591L676 681V703C649 672 612 649 570 649C533 649 492 658 453 665C397 677 340 686 283 686C216 686 149 665 102 617C63 578 32 529 32 474C32 434 43 392 75 367L139 431C103 445 75 477 75 516C75 540 85 563 102 580C134 612 179 623 224 623C278 623 332 614 384 596C353 566 326 533 302 497C284 468 269 438 261 404C267 372 306 327 336 293C349 278 361 262 371 244C378 233 384 221 384 207C384 189 375 173 364 159C349 140 330 124 309 112C282 119 253 119 224 117C181 82 140 45 102 5L112 -11C134 6 156 21 181 33C198 41 216 48 235 48C267 48 297 36 325 21C364 0 404 -21 448 -27C477 -13 504 6 529 28C561 55 590 85 618 117L607 133Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.697,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,13.84,0)"><path d="M228 641L116 558C119 502 116 446 116 389H62L26 353H114C113 256 112 63 112 62L212 -21L349 78L346 100C324 89 283 69 282 69C274 67 266 69 259 73C240 84 217 105 197 123C195 170 195 276 195 353H272L302 389H196C196 454 197 518 208 582C209 589 210 596 215 601L242 627L228 641Z"></path></g><g transform="matrix(.013,0,0,-0.013,18.169,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g></svg> and <svg height="9.14241pt" id="M282" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -5.96091 12.001 9.14241" width="12.001pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M515 96L502 119C471 88 431 62 423 62C416 62 411 70 417 101C440 223 469 341 497 448H486L412 422L380 277C330 188 210 57 152 57C137 57 126 69 139 124L195 366C210 431 205 448 182 448C155 448 89 413 23 350L36 326C73 354 103 376 112 376C118 376 118 365 113 340L61 118C54 90 52 68 52 51C52 0 75 -12 98 -12S151 -3 181 17C242 58 305 119 362 193H364L345 104C323 3 339 -12 359 -12C390 -12 464 35 515 96Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.929,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g></svg> simultaneously on cubic Mandelbrot set.</div>

Journal of Function Spaces

fig12

Figure 12

Figure 12: Julia and Mandelbrot Sets of Transcendental Function via Fibonacci-Mann Iteration 