Mandelbrot Iteration Orbits by Ben Sparks
Loading the math board and drawing, please wait…
This example demonstrates the Mandelbrot iteration process and the famous Mandelbrot set. By iterating complex numbers, observe how points' trajectories map onto the set. Utilizes conditional statements and segment construction commands. Suitable for high school and above students learning complex numbers and fractal geometry.
GeoGebra Commands & Parameters
If(a ≟ 0, c, A1^(2) + c) → A2Segment(A1, A2) → B2Segment(A2, A3) → B3Segment(A3, A4) → B4Segment(A4, A5) → B5Segment(A5, A6) → B6Segment(A6, A7) → B7Segment(A7, A8) → B8Segment(A8, A9) → B9Segment(A9, A10) → B10Segment(A10, A11) → B11Segment(A11, A12) → B12Segment(A12, A13) → B13Segment(A13, A14) → B14Segment(A14, A15) → B15Segment(A15, A16) → B16Segment(A16, A17) → B17Segment(A17, A18) → B18Segment(A18, A19) → B19Segment(A19, A20) → B20Segment(A20, A21) → B21Segment(A21, A22) → B22Segment(A22, A23) → B23Segment(A23, A24) → B24Segment(A24, A25) → B25Segment(A25, A26) → B26Segment(A26, A27) → B27Segment(A27, A28) → B28Segment(A28, A29) → B29Segment(A29, A30) → B30Segment(A30, A31) → B31Segment(A31, A32) → B32Segment(A32, A33) → B33Segment(A33, A34) → B34Segment(A34, A35) → B35Segment(A35, A36) → B36Segment(A36, A37) → B37Segment(A37, A38) → B38Segment(A38, A39) → B39Segment(A39, A40) → B40Segment(A40, A41) → B41Segment(A41, A42) → B42Segment(A42, A43) → B43Segment(A43, A44) → B44Segment(A44, A45) → B45Segment(A45, A46) → B46Segment(A46, A47) → B47Segment(A47, A48) → B48Segment(A48, A49) → B49Segment(A49, A50) → B50Segment(A50, A51) → B51Segment(A51, A52) → B52Segment(A52, A53) → B53Segment(A53, A54) → B54Segment(A54, A55) → B55Segment(A55, A56) → B56Segment(A56, A57) → B57Segment(A57, A58) → B58Segment(A58, A59) → B59Segment(A59, A60) → B60Segment(A60, A61) → B61Segment(A61, A62) → B62Segment(A62, A63) → B63Segment(A63, A64) → B64Segment(A64, A65) → B65Segment(A65, A66) → B66Segment(A66, A67) → B67Segment(A67, A68) → B68Segment(A68, A69) → B69Segment(A69, A70) → B70Segment(A70, A71) → B71Segment(A71, A72) → B72Segment(A72, A73) → B73Segment(A73, A74) → B74Segment(A74, A75) → B75Segment(A75, A76) → B76Segment(A76, A77) → B77Segment(A77, A78) → B78Segment(A78, A79) → B79Segment(A79, A80) → B80Segment(A80, A81) → B81Segment(A81, A82) → B82Segment(A82, A83) → B83Segment(A83, A84) → B84Segment(A84, A85) → B85Segment(A85, A86) → B86Segment(A86, A87) → B87Segment(A87, A88) → B88Segment(A88, A89) → B89Segment(A89, A90) → B90Segment(A90, A91) → B91Segment(A91, A92) → B92Segment(A92, A93) → B93Segment(A93, A94) → B94Segment(A94, A95) → B95Segment(A95, A96) → B96Segment(A96, A97) → B97Segment(A97, A98) → B98Segment(A98, A99) → B99Segment(A99, A100) → B100Segment(A100, A101) → B101Segment(A101, A102) → B102Segment(A102, A103) → B103Segment(A103, A104) → B104Segment(A104, A105) → B105Segment(A105, A106) → B106Segment(A106, A107) → B107Segment(A107, A108) → B108Segment(A108, A109) → B109Segment(A109, A110) → B110Segment(A110, A111) → B111Segment(A111, A112) → B112Segment(A112, A113) → B113Segment(A113, A114) → B114Segment(A114, A115) → B115Segment(A115, A116) → B116Segment(A116, A117) → B117Segment(A117, A118) → B118Segment(A118, A119) → B119Segment(A119, A120) → B120Segment(A120, A121) → B121Segment(A121, A122) → B122Segment(A122, A123) → B123Segment(A123, A124) → B124Segment(A124, A125) → B125Segment(A125, A126) → B126Segment(A126, A127) → B127Segment(A127, A128) → B128Segment(A128, A129) → B129Segment(A129, A130) → B130Segment(A130, A131) → B131Segment(A131, A132) → B132Segment(A132, A133) → B133Segment(A133, A134) → B134Segment(A134, A135) → B135Segment(A135, A136) → B136Segment(A136, A137) → B137Segment(A137, A138) → B138Segment(A138, A139) → B139Segment(A139, A140) → B140Segment(A140, A141) → B141Segment(A141, A142) → B142Segment(A142, A143) → B143Segment(A143, A144) → B144Segment(A144, A145) → B145Segment(A145, A146) → B146Segment(A146, A147) → B147Segment(A147, A148) → B148Segment(A148, A149) → B149Segment(A149, A150) → B150Segment(A150, A151) → B151Segment(A151, A152) → B152Segment(A152, A153) → B153Segment(A153, A154) → B154Segment(A154, A155) → B155
AI Drawing Prompt Reference
Draw the iteration trajectory of the Mandelbrot set. Start from point A1, calculate A1 squared plus constant c. If a is not 0, assign the result to A2; otherwise, A2 equals c. Then, draw a line segment from A1 to A2. Repeat this process, generating a new point and drawing a line segment from the previous point to the new one, until 48 line segments are drawn, forming a complex trajectory.
The prompt above was compiled from the original drawing commands and is for reference only.