By LAS VEGAS – Chia seeds sprouted in trays have experimentally confirmed a mathematical model proposed by computer scientist and polymath Alan Turing decades ago. The model describes how patterns might emerge in desert vegetation, leopard spots and zebra stripes.
These and other blotchy and stripy features in nature are examples of what are called Turing patterns, so named because in 1952, Turing presented equations for how simple interactions between competing factors can lead to surprisingly complex surface patterns. In the case of arid regions, the competition for moisture among plants would drive the intricate distribution of vegetation.
border: 1px solid #ffcccb;
color: white;
margin-top: 50px;
background-image: url(“/wp-content/themes/sciencenews/client/src/images/[email protected]”);
padding: 20px;
clear: both;
}
.zephr-registration-form{max-width:440px;margin:20px auto;padding:20px;background-color:#fff;font-family:var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont)}.zephr-registration-form *{box-sizing:border-box}.zephr-registration-form-text > *{color:var(–zephr-color-text-main)}.zephr-registration-form-relative-container{position:relative}.zephr-registration-form-flex-container{display:flex}.zephr-registration-form-input.svelte-blfh8x{display:block;width:100%;height:calc(var(–zephr-input-height) * 1px);padding-left:8px;font-size:16px;border:calc(var(–zephr-input-borderWidth) * 1px) solid var(–zephr-input-borderColor);border-radius:calc(var(–zephr-input-borderRadius) * 1px);transition:border-color 0.25s ease, box-shadow 0.25s ease;outline:0;color:var(–zephr-color-text-main);background-color:#fff;font-family:var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont)}.zephr-registration-form-input.svelte-blfh8x::placeholder{color:var(–zephr-color-background-tinted)}.zephr-registration-form-input-checkbox.svelte-blfh8x{width:auto;height:auto;margin:8px 5px 0 0;float:left}.zephr-registration-form-input-radio.svelte-blfh8x{position:absolute;opacity:0;cursor:pointer;height:0;width:0}.zephr-registration-form-input-color[type=”color”].svelte-blfh8x{width:50px;padding:0;border-radius:50%}.zephr-registration-form-input-color[type=”color”].svelte-blfh8x::-webkit-color-swatch{border:none;border-radius:50%;padding:0}.zephr-registration-form-input-color[type=”color”].svelte-blfh8x::-webkit-color-swatch-wrapper{border:none;border-radius:50%;padding:0}.zephr-registration-form-input.disabled.svelte-blfh8x,.zephr-registration-form-input.disabled.svelte-blfh8x:hover{border:calc(var(–zephr-input-borderWidth) * 1px) solid var(–zephr-input-borderColor);background-color:var(–zephr-color-background-tinted)}.zephr-registration-form-input.error.svelte-blfh8x{border:1px solid var(–zephr-color-warning-main)}.zephr-registration-form-input-label.svelte-1ok5fdj.svelte-1ok5fdj{margin-top:10px;display:block;line-height:30px;font-size:12px;color:var(–zephr-color-text-tinted);font-family:var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont)}.zephr-registration-form-input-label.svelte-1ok5fdj span.svelte-1ok5fdj{display:block}.zephr-registration-form-button.svelte-17g75t9{height:calc(var(–zephr-button-height) * 1px);line-height:0;padding:0 20px;text-decoration:none;text-transform:capitalize;text-align:center;border-radius:calc(var(–zephr-button-borderRadius) * 1px);font-size:calc(var(–zephr-button-fontSize) * 1px);font-weight:normal;cursor:pointer;border-style:solid;border-width:calc(var(–zephr-button-borderWidth) * 1px);border-color:var(–zephr-color-action-tinted);transition:backdrop-filter 0.2s, background-color 0.2s;margin-top:20px;display:block;width:100%;background-color:var(–zephr-color-action-main);color:#fff;position:relative;overflow:hidden;font-family:var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont)}.zephr-registration-form-button.svelte-17g75t9:hover{background-color:var(–zephr-color-action-tinted);border-color:var(–zephr-color-action-tinted)}.zephr-registration-form-button.svelte-17g75t9:disabled{background-color:var(–zephr-color-background-tinted);border-color:var(–zephr-color-background-tinted)}.zephr-registration-form-button.svelte-17g75t9:disabled:hover{background-color:var(–zephr-color-background-tinted);border-color:var(–zephr-color-background-tinted)}.zephr-registration-form-text.svelte-i1fi5{font-size:19px;text-align:center;margin:20px auto;font-family:var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont)}.zephr-registration-form-input-inner-text.svelte-lvlpcn{cursor:pointer;position:absolute;top:50%;transform:translateY(-50%);right:10px;color:var(–zephr-color-text-main);font-size:12px;font-weight:bold;font-family:var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont)}.zephr-registration-form-divider-container.svelte-mk4m8o{display:flex;align-items:center;justify-content:center;margin:40px 0}.zephr-registration-form-divider-line.svelte-mk4m8o{height:1px;width:50%;margin:0 5px;background-color:var(–zephr-color-text-tinted);;}.zephr-registration-form-divider-text.svelte-mk4m8o{margin:0 12px;color:var(–zephr-color-text-main);font-size:14px;font-family:var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont);white-space:nowrap}.zephr-registration-form-response-message.svelte-179421u{text-align:center;padding:10px 30px;border-radius:5px;font-size:15px;margin-top:10px;font-family:var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont)}.zephr-registration-form-response-message-title.svelte-179421u{font-weight:bold;margin-bottom:10px}.zephr-registration-form-response-message-success.svelte-179421u{background-color:#baecbb;border:1px solid #00bc05}.zephr-registration-form-response-message-error.svelte-179421u{background-color:#fcdbec;border:1px solid #d90c00}.zephr-recaptcha-tcs.svelte-1wyy3bx{margin:20px 0 0 0;font-size:15px;font-family:var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont)}.zephr-recaptcha-inline.svelte-1wyy3bx{margin:20px 0 0 0}.zephr-registration-form-social-sign-in.svelte-gp4ky7{align-items:center}.zephr-registration-form-social-sign-in-button.svelte-gp4ky7{height:55px;padding:0 15px;color:#000;background-color:#fff;box-shadow:0px 0px 5px rgba(0, 0, 0, 0.3);border-radius:10px;font-size:17px;display:flex;align-items:center;cursor:pointer;margin-top:20px;font-family:var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont)}.zephr-registration-form-social-sign-in-button.svelte-gp4ky7:hover{background-color:#fafafa}.zephr-registration-form-social-sign-in-icon.svelte-gp4ky7{display:flex;justify-content:center;margin-right:30px;width:25px}.zephr-form-link-message.svelte-rt4jae{margin:10px 0 10px 20px;font-family:var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont)}.zephr-registration-form-progress-bar.svelte-8qyhcl{width:100%;border:0;border-radius:20px;margin-top:10px}.zephr-registration-form-progress-bar.svelte-8qyhcl::-webkit-progress-bar{background-color:var(–zephr-color-background-tinted);border:0;border-radius:20px}.zephr-registration-form-progress-bar.svelte-8qyhcl::-webkit-progress-value{background-color:var(–zephr-color-text-tinted);border:0;border-radius:20px}.zephr-registration-progress-bar-step.svelte-8qyhcl{margin:auto;color:var(–zephr-color-text-tinted);font-size:12px;font-family:var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont)}.zephr-registration-progress-bar-step.svelte-8qyhcl:first-child{margin-left:0}.zephr-registration-progress-bar-step.svelte-8qyhcl:last-child{margin-right:0}.zephr-registration-form-input-inner-text.svelte-lvlpcn{cursor:pointer;position:absolute;top:50%;transform:translateY(-50%);right:10px;color:var(–zephr-color-text-main);font-size:12px;font-weight:bold;font-family:var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont)}.zephr-registration-form-input-error-text.svelte-19a73pq{color:var(–zephr-color-warning-main);font-family:var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont)}.zephr-registration-form-input-select.svelte-19a73pq{display:block;appearance:auto;width:100%;height:calc(var(–zephr-input-height) * 1px);font-size:16px;border:calc(var(–zephr-input-borderWidth) * 1px) solid var(–zephr-color-text-main);border-radius:calc(var(–zephr-input-borderRadius) * 1px);transition:border-color 0.25s ease, box-shadow 0.25s ease;outline:0;color:var(–zephr-color-text-main);background-color:#fff;padding:10px}.zephr-registration-form-input-select.disabled.svelte-19a73pq{border:1px solid var(–zephr-color-background-tinted)}.zephr-registration-form-input-select.unselected.svelte-19a73pq{color:var(–zephr-color-background-tinted)}.zephr-registration-form-input-select.error.svelte-19a73pq{border-color:var(–zephr-color-warning-main)}.zephr-registration-form-input-textarea.svelte-19a73pq{background-color:#fff;border:1px solid #ddd;color:#222;font-size:14px;font-weight:300;padding:16px;width:100%}.zephr-registration-form-input-slider-output.svelte-19a73pq{margin:13px 0 0 10px}.spin.svelte-1cj2gr0{animation:svelte-1cj2gr0-spin 2s 0s infinite linear}.pulse.svelte-1cj2gr0{animation:svelte-1cj2gr0-spin 1s infinite steps(8)}@keyframes svelte-1cj2gr0-spin{0%{transform:rotate(0deg)}100%{transform:rotate(360deg)}}.zephr-registration-form-input-radio.svelte-1qn5n0t{position:absolute;opacity:0;cursor:pointer;height:0;width:0}.zephr-registration-form-radio-label.svelte-1qn5n0t{display:flex;align-items:center;font-family:var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont)}.zephr-registration-form-radio-dot.svelte-1qn5n0t{position:relative;box-sizing:border-box;height:23px;width:23px;background-color:#fff;border:1px solid #ebebeb;border-radius:50%;margin-right:12px}.checked.svelte-1qn5n0t{border-color:#009fe3}.checked.svelte-1qn5n0t:after{content:””;position:absolute;width:17px;height:17px;background:#009fe3;background:linear-gradient(#009fe3, #006cb5);border-radius:50%;top:2px;left:2px}.disabled.checked.svelte-1qn5n0t:after{background:var(–zephr-color-background-tinted)}.error.svelte-1qn5n0t{border:1px solid var(–zephr-color-warning-main)}.zephr-registration-form-checkbox.svelte-1gzpw2y{position:absolute;opacity:0;cursor:pointer;height:0;width:0}.zephr-registration-form-checkbox-label.svelte-1gzpw2y{display:flex;align-items:center;font-family:var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont)}.zephr-registration-form-checkmark.svelte-1gzpw2y{position:relative;box-sizing:border-box;height:23px;width:23px;background-color:#fff;border:1px solid var(–zephr-color-text-main);border-radius:6px;margin-right:12px;cursor:pointer}.zephr-registration-form-checkmark.checked.svelte-1gzpw2y{border-color:#009fe3}.zephr-registration-form-checkmark.checked.svelte-1gzpw2y:after{content:””;position:absolute;width:6px;height:13px;border:solid #009fe3;border-width:0 2px 2px 0;transform:rotate(45deg);top:3px;left:8px;box-sizing:border-box}.zephr-registration-form-checkmark.disabled.svelte-1gzpw2y{border:1px solid var(–zephr-color-background-tinted)}.zephr-registration-form-checkmark.disabled.checked.svelte-1gzpw2y:after{border:solid var(–zephr-color-background-tinted);border-width:0 2px 2px 0}.zephr-registration-form-checkmark.error.svelte-1gzpw2y{border:1px solid var(–zephr-color-warning-main)}.zephr-registration-form-google-icon.svelte-1jnblvg{width:20px}.zephr-form-link.svelte-64wplc{margin:10px 0;color:#6ba5e9;text-decoration:underline;cursor:pointer;font-family:var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont)}.zephr-form-link-disabled.svelte-64wplc{color:var(–zephr-color-text-main);cursor:none;text-decoration:none}.zephr-registration-form-password-progress.svelte-d1zv9r{display:flex;margin-top:10px}.zephr-registration-form-password-bar.svelte-d1zv9r{width:100%;height:4px;border-radius:2px}.zephr-registration-form-password-bar.svelte-d1zv9r:not(:first-child){margin-left:8px}.zephr-registration-form-password-requirements.svelte-d1zv9r{margin:20px 0;justify-content:center}.zephr-registration-form-password-requirement.svelte-d1zv9r{display:flex;align-items:center;color:var(–zephr-color-text-tinted);font-size:12px;height:20px;font-family:var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont)}.zephr-registration-form-password-requirement-icon.svelte-d1zv9r{margin-right:10px;font-size:15px}.zephr-registration-form-password-progress.svelte-d1zv9r{display:flex;margin-top:10px}.zephr-registration-form-password-bar.svelte-d1zv9r{width:100%;height:4px;border-radius:2px}.zephr-registration-form-password-bar.svelte-d1zv9r:not(:first-child){margin-left:8px}.zephr-registration-form-password-requirements.svelte-d1zv9r{margin:20px 0;justify-content:center}.zephr-registration-form-password-requirement.svelte-d1zv9r{display:flex;align-items:center;color:var(–zephr-color-text-tinted);font-size:12px;height:20px;font-family:var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont)}.zephr-registration-form-password-requirement-icon.svelte-d1zv9r{margin-right:10px;font-size:15px}.zephr-registration-form {
max-width: 100%;
background-image: url(/wp-content/themes/sciencenews/client/src/images/[email protected]);
font-family: var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont);
margin: 0px auto;
margin-bottom: 4rem;
padding: 20px;
}
.zephr-registration-form-text h6 {
font-size: 0.8rem;
}
.zephr-registration-form h4 {
font-size: 3rem;
}
.zephr-registration-form h4 {
font-size: 1.5rem;
}
.zephr-registration-form-button.svelte-17g75t9:hover {
background-color: #fc6a65;
border-color: #fc6a65;
width: 150px;
margin-left: auto;
margin-right: auto;
}
.zephr-registration-form-button.svelte-17g75t9:disabled {
background-color: #e04821;
border-color: #e04821;
width: 150px;
margin-left: auto;
margin-right: auto;
}
.zephr-registration-form-button.svelte-17g75t9 {
background-color: #e04821;
border-color: #e04821;
width: 150px;
margin-left: auto;
margin-right: auto;
}
.zephr-registration-form-text > * {
color: #FFFFFF;
font-weight: bold
font: 25px;
}
.zephr-registration-form-progress-bar.svelte-8qyhcl {
width: 100%;
border: 0;
border-radius: 20px;
margin-top: 10px;
display: none;
}
.zephr-registration-form-response-message-title.svelte-179421u {
font-weight: bold;
margin-bottom: 10px;
display: none;
}
.zephr-registration-form-response-message-success.svelte-179421u {
background-color: #8db869;
border: 1px solid #8db869;
color: white;
margin-top: -0.2rem;
}
.zephr-registration-form-text.svelte-i1fi5:nth-child(1){
font-size: 18px;
text-align: center;
margin: 20px auto;
font-family: var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont);
color: white;
}
.zephr-registration-form-text.svelte-i1fi5:nth-child(5){
font-size: 18px;
text-align: left;
margin: 20px auto;
font-family: var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont);
color: white;
}
.zephr-registration-form-text.svelte-i1fi5:nth-child(7){
font-size: 18px;
text-align: left;
margin: 20px auto;
font-family: var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont);
color: white;
}
.zephr-registration-form-text.svelte-i1fi5:nth-child(9){
font-size: 18px;
text-align: left;
margin: 20px auto;
font-family: var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont);
color: white;
}
.zephr-registration-form-input-label.svelte-1ok5fdj span.svelte-1ok5fdj {
display: none;
color: white;
}
.zephr-registration-form-input.disabled.svelte-blfh8x, .zephr-registration-form-input.disabled.svelte-blfh8x:hover {
border: calc(var(–zephr-input-borderWidth) * 1px) solid var(–zephr-input-borderColor);
background-color: white;
}
.zephr-registration-form-checkbox-label.svelte-1gzpw2y {
display: flex;
align-items: center;
font-family: var(–zephr-typography-body-font), var(–zephr-typography-body-fallbackFont);
color: white;
font-size: 20px;
margin-bottom: -20px;
}
But proving that Turing’s model explains patterns in the real world has been challenging (SN: 10/21/15). It wasn’t clear whether Turing’s idea is really behind natural distributions of vegetation. It could be that the idea is a mathematical just-so story that happens to produce similar shapes in a computer, says physicist Flavio Fenton of Georgia Tech in Atlanta.
In research presented at the American Physical Society meeting, Brendan D’Aquino, who studied in Fenton’s lab during the summer of 2022, described an experiment that seems to confirm that Turing’s model truly underlies patterns in vegetation.
The team grew chia seeds in even layers in trays and then adjusted the available moisture. In essence, the researchers were experimentally tweaking the factors that appear in the Turing equations. Sure enough, patterns resembling those seen in natural environments emerged. The patterns also strongly resembled computer simulations of the Turing model.
“In previous studies,” said D’Aquino, who is an undergraduate computer science student at Northeastern University, “people kind of retroactively fit models to observe Turing patterns that they found in the world. But here we were actually able to show that changing the relevant parameters in the model produces experimental results that we would expect.”
Although Turing patterns have been produced in some chemistry experiments and other artificial systems, the team believes this is the first time that experiments with living vegetation have verified Turing’s mathematical insight.
