On a Generalization of Hofstadter’s <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.838901pt" id="M1" height="14.2383pt" version="1.1" viewBox="-0.0657574 -11.3994 12.5675 14.2383" width="12.5675pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-82" d="M699 368C699 549 574 666 407 666C186 666 23 488 23 277C23 113 129 -3 288 -13L307 -26C431 -111 501 -139 533 -147C559 -154 613 -163 658 -164L666 -141C597 -111 507 -66 430 -11L416 -1C580 42 699 190 699 368ZM601 371C601 227 518 54 381 22L354 40L278 24C175 47 120 145 120 269C120 451 235 631 398 631C540 631 601 521 601 371Z"/></g></svg>-Sequence: A Family of Chaotic Generational Structures

<div>Blue: <span class="nowrap"><svg height="13.639pt" id="M186" style="vertical-align:-4.35067pt" version="1.1" viewbox="-0.0498162 -9.28833 61.4923 13.639" width="61.4923pt" 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="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z" id="g113-223"></path></g><g transform="matrix(.013,0,0,-0.013,7.385,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path></g><g transform="matrix(.013,0,0,-0.013,11.883,0)"><path d="M480 416C480 431 465 448 438 448C388 448 312 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id="g113-42"></path></g></svg>.</span></div>

Complexity

fig9

Figure 9

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Complexity

On a Generalization of Hofstadter’s -Sequence: A Family of Chaotic Generational Structures

Figure 9